Brief Summary: The therapy of solid tumors has been revolutionized by immune therapy, in particular, approaches that activate immune T cells in a polyclonal manner through blockade of checkpoint pathways such as PD-1 by administration of monoclonal antibodies. In this study, the investigators will evaluate the adoptive transfer of RAPA-201 cells, which are checkpoint-deficient polyclonal T cells that represent an analogous yet distinct immune therapy treatment platform for solid tumors. RAPA-201 is a second-generation immunotherapy product consisting of reprogrammed autologous CD4+ and CD8+ T cells of Th1/Tc1 cytokine phenotype. First-generation RAPA-101, which was bred for resistance to the mTOR inhibitor rapamycin, demonstrated clear anti-tumor effects in multiple myeloma patients without any product-related adverse events. Second-generation RAPA-201, which have acquired resistance to the mTOR inhibitor temsirolimus, are manufactured ex vivo from peripheral blood mononuclear cells collected from solid tumor patients using a steady-state apheresis. RAPA-201 is also being evaluated for the therapy of relapsed, refractory multiple myeloma and was granted Fast Track Status by the FDA for this indication. The novel RAPA-201 manufacturing platform, which incorporates both an mTOR inhibitor (temsirolimus) and an anti-cancer Th1/Tc1 polarizing agent (IFN-alpha) generates polyclonal T cells with five key characteristics: 1. Th1/Tc1: polarization to anti-cancer Th1 and Tc1 subsets, with commensurate down-regulation of immune suppressive Th2 and regulatory T (TREG) subsets; 2. T Central Memory: expression of a T central memory (TCM) phenotype, which promotes T cell engraftment and persistence for prolonged anti-tumor effects; 3. Temsirolimus-Resistance: acquisition of temsirolimus-resistance, which translates into a multi-faceted anti-apoptotic phenotype that improves T cell fitness in the stringent conditions of the tumor microenvironment; 4. T Cell Quiescence: reduced T cell activation, as evidence by reduced expression of the IL-2 receptor CD25, which reduces T cell-mediated cytokine toxicities such as cytokine-release syndrome (CRS) that limit other forms of T cell therapy; and 5. Reduced Checkpoints: multiple checkpoint inhibitory receptors are markedly reduced on RAPA-201 cells (including but not limited to PD-1, CTLA4, TIM-3, LAG3, and LAIR1), which increases T cell immunity in the checkpoint-replete, immune suppressive tumor microenvironment. This is a Simon 2-stage, non-randomized, open label, multi-site, phase I/II trial of RAPA-201 T immune cell therapy in patients with advanced metastatic, recurrent, and unresectable solid tumors that have recurred or relapsed after prior immune therapy. Patients must have tumor relapse after at least one prior line of therapy and must have refractory status to the most recent regimen, which must include an anti-PD-(L)1 monoclonal antibody. Furthermore, accrual is limited to solid tumor disease types potentially amenable to standard-of-care salvage chemotherapy consisting of the carboplatin + paclitaxel (CP) regimen that will be utilized for host conditioning prior to RAPA-201 therapy. Importantly, carboplatin and paclitaxel are "immunogenic" chemotherapy agents whereby the resultant cancer cell death mechanism is favorable for generation of anti-tumor immune T cell responses. Thus, the CP regimen that this protocol incorporates is intended to directly control tumor progression and indirectly promote anti-tumor T cell immunity. The CP regimen is considered standard-of-care therapy for the following tumor types, which will be focused upon on this RAPA-201 protocol: small cell and non-small cell lung cancer; breast cancer (triple-negative sub-type or relapse after ovarian ablation/suppression); gastric cancer (esophageal and esophageal-gastric-junction adenocarcinoma; gastric adenocarcinoma; esophageal squamous cell carcinoma); head and neck cancer (squamous cell carcinoma of oral cavity, larynx, nasopharynx, and other sites); carcinoma of unknown primary; bladder cancer; and malignant melanoma. Protocol therapy consists of six cycles of standard-of-care chemotherapy (carboplatin + paclitaxel (CP) regimen) administered every 28 days (chemotherapy administered on cycles day 1, 8, and 15). RAPA-201 cells will be administered at a target flat dose of 400 X 10\^6 cells per infusion on day 3 of cycles 2 through 6. A sample size of up to 22 patients was selected to determine whether RAPA-201 therapy, when used in combination with the CP regimen, represents an active regimen in solid tumors that are resistant to anti-PD(L)-1 checkpoint inhibitor therapy, as defined by a response rate (≥ PR) consistent with a rate of 35%. The first stage of protocol accrual will consist of n=10 patients; to advance to the second protocol accrual stage, RAPA-201 therapy must result in a tumor response (≥ PR) in at least 2 out of the 10 initial patients.

Detailed Description: The therapy of solid tumors has been revolutionized by immune therapy, in particular, approaches that activate immune T cells in a polyclonal manner through blockade of checkpoint pathways such as PD-1 by administration of monoclonal antibodies. In this study, the investigators will evaluate the adoptive transfer of a reprogrammed T cell population termed RAPA-201 cells, which are checkpoint-deficient polyclonal T cells that represent an analogous yet distinct treatment platform for solid tumor immune therapy. RAPA-201 is a second-generation T cell immunotherapy product that is comprised of autologous CD4+ and CD8+ T cells of Th1/Tc1 cytokine phenotype. The first-generation RAPA-101 product, which was bred for resistance to the mTOR inhibitor rapamycin and developed for therapy of multiple myeloma, demonstrated clear anti-tumor effects without any product-related adverse events. The second-generation RAPA-201 cells, which have acquired resistance to the mTOR inhibitor temsirolimus, are manufactured ex vivo from peripheral blood mononuclear cells collected from solid tumor patients using a steady-state apheresis. RAPA-201 cells are also being evaluated for the therapy of relapsed, refractory multiple myeloma and was granted Fast Track Status by the FDA for this indication. The novel method of RAPA-201 manufacturing, which incorporates both an mTOR inhibitor (temsirolimus) and an anti-cancer Th1/Tc1 polarizing agent (IFN-alpha) generates a polyclonal T cell population with the following five key characteristics: 1. Th1/Tc1: polarization to the anti-cancer Th1 and Tc1 subsets, with commensurate down-regulation of immune suppressive Th2 and regulatory T (TREG) subsets; 2. T Central Memory: expression of a T central memory (TCM) phenotype, which promotes T cell engraftment and persistence necessary for prolonged anti-tumor effects; 3. Temsirolimus-Resistance: acquisition of temsirolimus-resistance, which translates into a multi-faceted anti-apoptotic phenotype that improves T cell fitness in the stringent conditions of the tumor microenvironment; 4. T Cell Quiescence: reduced T cell activation, as evidence by reduced expression of the IL-2 receptor CD25, which reduces the chance of T cell-mediated cytokine toxicities such as cytokine-release syndrome (CRS) that limit other forms of T cell therapy; and 5. Reduced Checkpoints: multiple checkpoint inhibitory receptors are markedly reduced on RAPA-201 cells (including but not limited to PD-1, CTLA4, TIM-3, LAG3, and LAIR1), which increases T cell immunity in the checkpoint-replete, immune suppressive tumor microenvironment. This is a multi-site phase I/II study evaluating RAPA-201 cells in up to 22 patients with relapsed solid tumors who have disease progression after anti-PD1 pathway monoclonal antibody therapy. The study will evaluate adoptive T cell therapy using autologous rapamycin-resistant Th1/Tc1 cells (RAPA-201) in the context of a standard-of-care chemotherapy regimen comprised of carboplatin plus paclitaxel (CP Regimen). The study will only accrue patients with solid tumor types that support use of the CP Regimen as a salvage therapy. Importantly, carboplatin and paclitaxel are considered "immunogenic" chemotherapy whereby the resultant cancer cell death mechanism is favorable for the generation of anti-tumor immune T cell responses. Therefore, the CP regimen that this protocol incorporates is intended to both directly control tumor progression and indirectly promote anti-tumor T cell immunity. The CP regimen is considered standard-of-care therapy for the following tumor types, which will therefore be focused upon on this RAPA-201 protocol: small cell and non-small cell lung cancer; breast cancer (triple-negative sub-type or relapse after ovarian ablation/suppression); gastric cancer (esophageal and esophageal-gastric-junction adenocarcinoma; gastric adenocarcinoma; esophageal squamous cell carcinoma); head and neck cancer (squamous cell carcinoma of oral cavity, larynx, nasopharynx, and other sites); carcinoma of unknown primary; bladder cancer; and malignant melanoma. To be eligible for the protocol, a subject will be required to have a circulating absolute lymphocyte count (ALC) of ≥ 300 cells per microliter. This parameter will help ensure that a sufficient number of autologous RAPA-201 cells can be manufactured from a steady-state apheresis product. Once the apheresis product has been received at the manufacturing site, the subject can initiate the first cycle of the CP Regimen, which will be administered over a 28-day interval. Within 10 days after positive determination of study eligibility (and subject enrollment), two key actions will occur: (1) T cells will be collected by steady-state apheresis and sent to the manufacturing site at Rapa Therapeutics; (2) and the patient will start Cycle 1 of the CP Regimen (with a window of up to 7 calendar days to begin). The Carboplatin-Paclitaxel (CP) regimen will be given alone for Cycle 1 and in combination with RAPA-201 cells for Cycles 2-6. After the completion of the treatment portion of the study, the subject will enter the follow-up component that will last for 6 months. Cycle 1 of the CP Regimen will be a 28-day cycle, which will allow for time to manufacture the RAPA-201 cell product. According to standard-of-care practice, the carboplatin and paclitaxel will be administered on days 1, 8, and 15 of each cycle. Each cycle, beginning with Cycle 1, may be delayed or extended for up to four weeks, if needed for various reasons, including: logistical considerations, resolution of adverse events, or if there is a delay in RAPA-201 manufacturing. Requests for using additional time between cycles, other than the visit windows specified in the Schedule of Events, should be approved by the Medical Monitor. Cycles 2-6 will also be 28-day cycles but will include both the CP Regimen plus the infusion of RAPA-201 cells at a target flat dose of 400 X 10\^6 cells per infusion. A sample size of up to 22 patients was selected to determine whether RAPA-201 therapy, when used in combination with the CP regimen, represents an active regimen in solid tumors that are resistant to anti-PD(L)-1 checkpoint inhibitor therapy, as defined by achieving a response rate (≥ PR) consistent with a rate of 35%. The first stage of protocol accrual will consist of n=10 patients; to advance to the second stage of protocol accrual, RAPA-201 therapy must result in a tumor response (≥ PR) in at least 2 out of the 10 initial patients.