Brief Summary: The purpose of this study is to find the number of natural killer (NK) cells from non-HLA matched donors that can be safely infused into patients with cancer. NK cells are a form of lymphocytes that defend against cancer cells. NK cells in cancer patients do not work well to fight cancer. In this study, the NK cells are being donated by healthy individuals without cancer who are not "matched" by human leukocyte antigen (HLA) genes to patients. After receiving these NK cells, patients may also be given a drug called ALT803. ALT803 is a protein that keeps NK cells alive, helps them grow in number and supports their cancer-fighting characteristics. HLA-unmatched NK cell infusion is investigational (experimental) because the process has not approved by the Food and Drug Administration (FDA).

Detailed Description: Primary Objective: To determine the maximum tolerated dose (MTD) of ex vivo expanded non-HLA matched donor NK cells in combination with ALT-803 Secondary Objectives: * Describe safety profile / toxicity of combining ALT-803 with NK cell adoptive therapy. * Determine antitumor activity of allogeneic NK cells with ALT-803 support. * Determine if a lymphocyte depleting regimen is adequate for preventing early elimination of HLA-mismatched donor NK cells by host T-cells. Study Design: This is a phase I study with "3+3" design with three planned dose levels of NK cells and a fixed dose of ALT-803. Three patients will be enrolled sequentially to each dose level, starting with dose level 1. Patients will be segregated to either receive ALT803 as cytokine support after NK cell infusion (starting with same dose level as Level 1) or no cytokine administration. Patients in the arm receiving ALT803 will be either hematologic malignancy patients (Cohort A) or Colon/Soft tissue sarcoma patients (Cohort B). Absence of dose limiting toxicity (DLT) in the DLT assessment period of 28 days must be documented for all patients enrolled a cell dose without ALT803 before the next cohort of patients to receive cytokines at that dose level can be enrolled. Patients can also be enrolled in parallel to the next cell dose level without cytokines.