Study of the Safety of Therapeutic Tx With Immunomodulatory MSC in Adults With COVID-19 Infection Requiring Mechanical Ventilation

Inclusion Criteria: 1. Age ≥ 18 years old. 2. Able to understand and provide a signed informed consent that fulfills the relevant Institutional Review Board (IRB) or Independent Ethics Committee (IEC) guidelines. For subjects that are intubated and/or sedated, or otherwise unable to provide consent, prospective consent from a legally-authorized representative is required. The subject or his/her legally authorized representative must be able to provide consent. 3. Has laboratory-confirmed positive novel coronavirus (SARS-CoV-2) test, as determined by polymerase chain reaction (PCR), or other commercial or public health assay in any specimen \< 72 hours prior to enrollment, or meets the criteria to guide the evaluation and testing of patients under investigation (PUI) for COVID-19 (https://emergency.cdc.gov/han/2020/HAN00428.asp). 4. Requiring mechanical ventilatory support with moderate to severe Acute Respiratory Distress Syndrome (ARDS) as determined by the Berlin criteria: 1. Bilateral opacities present on a chest radiograph or computed tomographic (CT) scan. These opacities are not fully explained by pleural effusions, lobar collapse, lung collapse, or pulmonary nodules. 2. Origin of Edema: Respiratory failure not fully explained by cardiac failure or fluid overload. 3. Oxygenation: Moderate to severe impairment of oxygenation must be present, as defined by the ratio of arterial oxygen tension to fraction of inspired oxygen (PaO2/FiO2). The severity of the hypoxemia defines the severity of the ARDS: * Moderate: PaO2/FiO2 \>100 mmHg and ≤ 200 mmHg, on ventilator settings that include PEEP ≥ 5 cm H2O * Severe: PaO2/FiO2 ≤100 mmHg on ventilator settings that include PEEP ≥5 cm H2O Subjects receiving extracorporeal membrane oxygenation (ECMO) will not be enrolled in this study. 5. High-sensitivity C-reactive Protein (hs-CRP) serum level \> 4.0 mg/dL 6. Acute Physiology and Chronic Health Evaluation (APACHE IV) score \> 5 7. Agrees to the collection of nasopharyngeal (NP) swabs and venous blood per protocol. 8. Ability to attend required study visits and return for adequate follow-up, as required by this protocol. 9. Agreement to practice effective contraception for female subjects of child-bearing potential and non-sterile males. Female subjects of child-bearing potential must agree to use effective contraception while on study and for at least 1 month after the last dose of BM-Allo.MSC. Non-sterile male subjects must agree to use a condom while on study and for up to 1 month after the dose of BM-Allo.MSC. Effective contraception includes surgical sterilization (eg, vasectomy, tubal ligation), two forms of barrier methods (eg, condom, diaphragm) used with spermicide, intrauterine devices (IUDs), oral contraceptives, and abstinence. Exclusion Criteria: 1. Known hypersensitivity to any component of the study medication(s). 2. Signs of multisystem organ failure. Liver function tests (LFTs) \> 5x normal. 3. Intubated \> 72 continuous hours. 4. Assessed by the Investigator to be unable or unwilling to comply with the requirements of the protocol. 5. Pregnant and nursing women. A negative serum pregnancy test during screening (within 72 hours prior to the first dose) must be documented before MSCs are administered to a female subject of child-bearing potential.