Study: NCT02423915

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: 375 mg/m2 by vein on Day -12 for for participants with CD20+ malignancies.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: 375 mg/m2 by vein on Day -12 for for participants with CD20+ malignancies.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: 375 mg/m2 by vein on Day -12 for for participants with CD20+ malignancies.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Rituximab
Description: 375 mg/m2 by vein on Day -12 for for participants with CD20+ malignancies.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Fludarabine
Description: 40 mg/m2 by vein on Days -8 to -5.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Fludarabine
Description: 40 mg/m2 by vein on Days -8 to -5.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Fludarabine
Description: 40 mg/m2 by vein on Days -8 to -5.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Fludarabine
Description: 40 mg/m2 by vein on Days -8 to -5.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Cyclophosphamide
Description: 50 mg/kg by vein on Day -8.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Cyclophosphamide
Description: 50 mg/kg by vein on Day -8.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Cyclophosphamide
Description: 50 mg/kg by vein on Day -8.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Cyclophosphamide
Description: 50 mg/kg by vein on Day -8.

Intervention type: RADIATION
Group type: EXPERIMENTAL
Intervention: Total Body Radiation
Description: 2 Gy delivered on Day -4.

Intervention type: RADIATION
Group type: EXPERIMENTAL
Intervention: Total Body Radiation
Description: 2 Gy delivered on Day -4.

Intervention type: RADIATION
Group type: EXPERIMENTAL
Intervention: Total Body Radiation
Description: 2 Gy delivered on Day -4.

Intervention type: RADIATION
Group type: EXPERIMENTAL
Intervention: Total Body Radiation
Description: 2 Gy delivered on Day -4.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Fucosylated Regulatory T Cells
Description: Phase I: Participants treated at cell dose level 1: 1 x 10\^6/kg Fucosylated T-reg cells on Day -1.~Phase II: Participants treated at cell dose level 2: 1 x 10\^7/kg Fucosylated T-reg cells on Day -1.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Fucosylated Regulatory T Cells
Description: Phase I: Participants treated at cell dose level 1: 1 x 10\^6/kg Fucosylated T-reg cells on Day -1.~Phase II: Participants treated at cell dose level 2: 1 x 10\^7/kg Fucosylated T-reg cells on Day -1.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusions
Description: Cord blood transplant, MRD, or MUD infused on Day 0.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusions
Description: Cord blood transplant, MRD, or MUD infused on Day 0.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusions
Description: Cord blood transplant, MRD, or MUD infused on Day 0.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Cord Blood Infusions
Description: Cord blood transplant, MRD, or MUD infused on Day 0.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate mofetil
Description: 15 mg/kg (actual body weight with a maximum dose of 1 gram twice daily) by vein or mouth from Day -3 to Day +100 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate mofetil
Description: 15 mg/kg (actual body weight with a maximum dose of 1 gram twice daily) by vein or mouth from Day -3 to Day +100 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate mofetil
Description: 15 mg/kg (actual body weight with a maximum dose of 1 gram twice daily) by vein or mouth from Day -3 to Day +100 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Mycophenolate mofetil
Description: 15 mg/kg (actual body weight with a maximum dose of 1 gram twice daily) by vein or mouth from Day -3 to Day +100 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Sirolimus
Description: 12 mg by mouth load followed by 4 mg by mouth daily from Day -3 to Day +180 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Sirolimus
Description: 12 mg by mouth load followed by 4 mg by mouth daily from Day -3 to Day +180 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Sirolimus
Description: 12 mg by mouth load followed by 4 mg by mouth daily from Day -3 to Day +180 in the absence of GVHD.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: Sirolimus
Description: 12 mg by mouth load followed by 4 mg by mouth daily from Day -3 to Day +180 in the absence of GVHD.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Bone Marrow Aspiration
Description: Bone marrow aspiration performed at 1, 3, 6, and 12 months after transplant to check status of disease.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Bone Marrow Aspiration
Description: Bone marrow aspiration performed at 1, 3, 6, and 12 months after transplant to check status of disease.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Bone Marrow Aspiration
Description: Bone marrow aspiration performed at 1, 3, 6, and 12 months after transplant to check status of disease.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Bone Marrow Aspiration
Description: Bone marrow aspiration performed at 1, 3, 6, and 12 months after transplant to check status of disease.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg/day subcutaneously beginning on D+0, and continuing until absolute neutrophil count (ANC) is \> 500 x 10/L for 3 consecutive days.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg/day subcutaneously beginning on D+0, and continuing until absolute neutrophil count (ANC) is \> 500 x 10/L for 3 consecutive days.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg/day subcutaneously beginning on D+0, and continuing until absolute neutrophil count (ANC) is \> 500 x 10/L for 3 consecutive days.

Intervention type: DRUG
Group type: EXPERIMENTAL
Intervention: G-CSF
Description: 5 mcg/kg/day subcutaneously beginning on D+0, and continuing until absolute neutrophil count (ANC) is \> 500 x 10/L for 3 consecutive days.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Non-Fucosylated Regulatory T Cells
Description: Phase I: Participants treated at cell dose level 1: 1 x 10\^7/kg Non-Fucosylated T-reg cells on Day -1.~Phase II: Participants treated at cell dose level 2: 1 x 10\^7/kg Non-Fucosylated T-reg cells on Day -1.

Intervention type: PROCEDURE
Group type: EXPERIMENTAL
Intervention: Non-Fucosylated Regulatory T Cells
Description: Phase I: Participants treated at cell dose level 1: 1 x 10\^7/kg Non-Fucosylated T-reg cells on Day -1.~Phase II: Participants treated at cell dose level 2: 1 x 10\^7/kg Non-Fucosylated T-reg cells on Day -1.