Anti-SARS Cov-2 T Cell Infusions for COVID 19

The first part of this study is to identify the maximum tolerated dose (MTD) of allogeneic SARS-CoV2-specific T cells (SARS-CoVSTs) for patients with COVID19 with high risk of progression to mechanical ventilation. The 3 dose levels (DL) are: DL1: 1x10\^7 cells (flat dose) DL2: 2x10\^7 cells (flat dose) DL3: 4x10\^7 cells (flat dose) Enrollment to the dose escalation phase will be staggered. The first patient enrolled on each of the 3 dose levels (DL1, DL2 and DL3) will have to complete the 14-day toxicity monitoring window prior to enrollment of the next patients. Prior to dose escalation, all patients at a particular dose level should have completed the minimum 14-day toxicity monitoring window before enrolling to a higher dose level. After the dose finding phase is complete and the MTD established, a randomized trial will be conducted. Patient will be randomized 1:1 using the permuted block method with a block size of 4 (2 in the treatment arm and 2 in the control arm) to receive treatment with SARS-CoVSTs or routine treatment per institutional standards. All enrolled patients will undergo the following evaluations: * Physical exam and history including height and weight * SARS-CoV-2 test * Blood tests * Chest X-ray or chest CT Scan if not already done in the past 48 hours. * A urine pregnancy test, when applicable Patients randomized to receive SARS-CoVSTs will be pre-medicated with Benadryl and Tylenol. The cells will be thawed and given through an intravenous line. Patients will be monitored for infusion side effects for up to 14 days or until infusion side effects have completely resolved, whichever is longer. Blood will be drawn before the infusion and then up to daily for 14 days or until the patient is discharged from the hospital. Optional blood samples will be drawn at 2, 3 and 6 months after infusion. Study participation will last 6 months after the date of infusion.