REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Mouse anti-human CD1d-unconjugated (clone 51.1)	Biolegend	Cat# 350321; RRID:
Mouse anti-human CD1d- APC (clone 51.1)	Biolegend	Cat# 350308; RRID:AB_10642829
Mouse anti-human CD1d-PE (clone 51.1),	Thermo Fisher Scientific	Cat# 12-0016-42; RRID:
Mouse anti-human CD3-FITC (clone SK7)	BD Biosciences	Cat# 345763; RRID:AB_2811220
Mouse anti-human CD3− APC (clone SK7)	BD Biosciences	Cat# 345767; RRID:AB_2833003
Mouse anti-human CD3-APC-H7 (clone SK7)	BD Biosciences	Cat# 560176; RRID:AB_1645475
Mouse anti-human CD3-BV421 (clone SK7)	BD Biosciences	Cat# 563797; RRID:AB_2744383
Mouse anti-human CD3-AF700 (clone SP34-2)	BD Biosciences	Cat# 557917; RRID:AB_396938
Mouse anti-human CD3-BUV395 (clone SP34-2)	BD Biosciences	Cat# 564117; RRID:AB_2738603
Mouse anti-human CD3-BV711 (clone UCHT1)	BD Biosciences	Cat# 563724; RRID:AB_2744392
Mouse anti-human CD5-BV605 (clone UCHT2)	BD Biosciences	Cat# 563945; RRID:AB_2738500
Mouse anti-human CD5-BV605 (clone L17F12)	Biolegend	Cat# 364020; RRID:AB_2565941
Mouse anti-human CD7-APC (clone M-T701)	BD Bioscience	Cat# 653311; RRID:AB_2870351
Mouse anti-human CD11b-PE-Cy7 (clone ICRF44)	BD Bioscience	Cat# 557743; RRID:AB_396849
Mouse anti-human CD13-BV421 (clone WM15)	BD biosciences	Cat# 562596; RRID:AB_2737672
Mouse anti-human CD14-FITC (clone MΦP9)	BD Biosciences	Cat# 345784; RRID:AB_2868810
Mouse anti-human CD14-PE-Dazzle594 (clone M5E2)	Biolegend	Cat# 301852; RRID:AB_2629576
Mouse anti-human CD14-PE-Cy7 (clone 63D3(	Biolegend	Cat# 367112; RRID:AB_2566714
Mouse anti-human CD19-PC7 (clone J3-119)	Beckman Coulter	Cat# IM3628
Mouse anti-human CD19-PE-CF594 (clone HIB19)	BD Biosciences	Cat# 562294; RRID:AB_11154408
Mouse anti-human CD19-APC (clone SJ25C1)	BD biosciences	Cat# 345791; RRID:AB_2868817
Mouse anti-human CD19-BV605 (clone SJ25C1)	BD biosciences	Cat# 740394; RRID:AB_2740124
Mouse anti-human CD20-FITC (clone 2H7)	BD Biosciences	Cat# 555622; RRID:AB_395988
Mouse anti-human CD20-AF700 (clone 2H7)	Biolegend	Cat# 303222
Mouse anti-human CD33-PE-CF594 (clone WM53)	BD Biosciences	Cat# 562492; RRID:AB_2713912
Mouse anti-human CD33-BV421 (clone WM53)	BD Biosciences	Cat# 562854; RRID:AB_2737405
Mouse anti-human CD34 PerCPCy5.5 (clone 8G12)	BD Biosciences	Cat# 347222; RRID:AB_2868843
Mouse anti-human CD34-APC (clone 581)	BD Biosciences	Cat# 555824; RRID:AB_398614
Mouse anti-human CD38-FITC (clone HB7)	BD Biosciences	Cat# 340909; RRID:AB_2868744
Mouse anti-human CD38-APC (clone HB7)	BD Biosciences	Cat# 340439; RRID:AB_400512
Mouse anti-human CD45-AF700 (clone HI30)	Biolegend	Cat# 304024; RRID:AB_493761
Mouse anti-human CD45-KO (clone J.33)	Beckman Coulter	Cat# B36294; RRID:AB_2833027
Mouse anti-human CD56-PC7 (clone N901)	Beckman Coulter	Cat# A21692; RRID:AB_2892144
Mouse anti-human CD56-APC (clone HCD56)	Biolegend	Cat# 318310; RRID:AB_604106
Mouse anti-human CD56-BV510 (clone NCAM16.2)	BD biosciences	Cat# 563041; RRID:AB_2732786
Mouse anti-human CD69-PE (clone FN50)	BD biosciences	Cat# 555531; RRID:AB_395916
Mouse anti-human CD69-APC-Fire750 (clone FN50)	Biolegend	Cat# 310946; RRID:AB_2616709
Mouse anti-human CD81 APC-H7 (clone JS-81)	BD Bioscience	Cat# 656647; RRID:AB_2870414
Mouse anti-human CD107a-PE (clone H4A3)	Miltenyi Biotec	Cat# 130-095-515; RRID:AB_10828805
Mouse anti-human CD107a-PE (clone H4A3)	Thermo Fischer Scientific	Cat# 12-1079-42; RRID:AB_10853326
Mouse anti-human CD117-PE-Cy7 (clone 104D2)	BD Biosciences	Cat# 339217; RRID:AB_2868720
Mouse anti-human CD117-APC (clone 104D2)	BD Biosciences	Cat# 333233; RRID:AB_2868677
Mouse anti-human CD117-BV650 (clone 104D2)	BD Biosciences	Cat# 563859; RRID:AB_2738453
Mouse anti-human CD138-FITC (clone MI15)	Biolegend	Cat# 356507; RRID:AB_2561881
Mouse anti-human CD138-BV421 (clone MI15)	BD biosciences	Cat# 562935; RRID:AB_2737904
Mouse anti-human TRAV10-PC7 (clone C15)	Beckman Coulter	Cat# A66907
Mouse anti-human TRBV25-1-PE (clone C21)	Beckman Coulter	Cat# IM2290; RRID:AB_131325
Mouse anti-human TRDV2-FITC (clone Immu389)	Beckman Coulter	Cat# IM1464; RRID:AB_131019
Mouse anti-human TRDV2-BV711 (clone B6)	Biolegend	Cat# 331412; RRID:AB_2565421
Mouse anti-human TRGV9-FITC (clone B3)	BD Biosciences	Cat# 555732; RRID:AB_396075
Mouse anti-human TRGV9-FITC (clone Immu360)	Beckman Coulter	Cat# IM1463; RRID:AB_130871
Mouse anti-human TRGV9-PE (clone B3)	Biolegend	Cat# 331308; RRID:AB_1236408
Mouse anti-human TRGV9-APC (clone B3)	Biolegend	Cat# 331310; RRID:AB_2057504
Mouse anti-human pan-γδTCR-BV421 (clone B1)	BD Bioscience	Cat# 562560; RRID:AB_2737655
Mouse anti-human HLA-DR-V450 (clone L243)	BioLegend	Cat# 655874; RRID:AB_2716783
Mouse anti-human HLA-DR-BV786 (clone L243)	BioLegend	Cat# 307642; RRID:AB_2563461
Goat anti-Llama IgG-heavy and light chain Antibody (GαL)-FITC (polyclonal)	Bethyl laboratories	Cat# A160-100F; RRID:AB_67106
Rabbit anti-Llama VHH (RαL)-iFluor488 (cocktail)	Genscript	Cat# A02021
Rabbit anti-Llama VHH (RαL)-iFluor555 mAb (clone 96A3F5)	Genscript	Cat# A01994
Rabbit anti-Llama VHH (RαL)-iFluor555 mAb (clone 96A3F5)	Genscript	Cat# A01863
Rat anti-mouse CD45-FITC (clone 30F11)	BD Biosciences	Cat# 553079; RRID:AB_394609
Rat anti-Mouse CD16/CD32-unconjugated (clone 2.4G2)	BD Biosciences	Cat# 553141; RRID:AB_394656
human FcR blocking reagent	Miltenyi Biotec	Cat# 130-059-901; RRID:AB_2892112
Biological samples
healthy human donor PBMC	Sanquin blood supply, the Netherlands	N/A
healthy human donor PBMC	AllCells, China	N/A
healthy human donor PBMC	Milestone Shanghai Biological Science & Technology, China	N/A
MM patient BMMC	Amsterdam UMC, the Netherlands	N/A
MM patient BMMC	Cureline tissue bank, San Francisco, USA	N/A
AML patient BMMC	Amsterdam UMC	N/A
AML patient BMMC	Centre de Ressources Biologiques des Hospices Civils, Lyon, France	N/A
CLL patient PBMC	Amsterdam UMC	N/A
M. fascicularis (origin China, Mauritius, and Vietnam) PBMC	CITox, Miserey, France	N/A
M. mulatta PBMC	CITox, Miserey, France	N/A
Chemicals, peptides, and recombinant proteins
α-GalCer	Avanti Polar Lipids	Cat# 867000P
OCH	AdipoGen	Cat # AG-CR1-3593
Sulfatide C24	Avanti Polar Lipids	Cat# 860871
CD1d(α-GalCer)-PE tetramer	Lameris et al., 202023	N/A
CD1d(α-GalCer)-APC tetramer	Lameris et al., 202023	N/A
CD1d(α-GalCer)-BV421 tetramer	Lameris et al., 202023	N/A
CD1d(α-GalCer)-BV711 tetramer	Lameris et al., 202023	N/A
CD1d(endogenous)-PE tetramer	Lameris et al., 202023	N/A
CD1d(sulfatide)-PE tetramer	Lameris et al., 202023	N/A
Thapsigargin	Sigma Aldrich	Cat# T9033
streptavidin-APC	Thermo Fischer Scientific	Cat# 17-4317-82
streptavidin-PE	Thermo Fischer Scientific	Cat# S866
NHS-D-biotin	Sigma Aldrich	Cat# H1759
7-amino-actinomycin D (7-AAD)	Sigma	Cat# A9400
Annexin V-FITC	VPS diagnostics	Cat# A700
pacific blue succinimidyl ester (PBSE)	Thermo Fisher Scientific	Cat# P10163
RPMI-1640	Gibco, Thermo Fisher Scientific	Cat# 22400089
IMDM	Gibco, Thermo Fisher Scientific	Cat# 12440061
DMEM	Gibco, Thermo Fisher Scientific	Cat# 41965039
FCS	Biological Industries	Cat# 04-007-1A
Human AB serum	MP biomedicals	Cat# 092930949
β-mercaptoethanol	Merck	Cat# 805740
sodium penicillin, streptomycin sulphate and L-glutamine (100×)	Gibco, Thermo Fisher Scientific	Cat# 10378016
Recombinant human IL-2	Novartis	N/A
Recombinant human IL-4	R&D Systems	Cat# 204-IL/CF
Recombinant human IL-7	R&D Systems	Cat# 207-IL-025
Recombinant human IL-15	eBioscience	Cat# 34-8159-85
GM-CSF	Sanofi Leukine	N/A
LPS	Sigma	Cat# L6529
phytohaemagglutinin (PHA)	Thermo Fisher Scientific	Cat# R30852801
Anti-CD1d VHH (clone VHH1D12)	Lameris et al., 202023	N/A
Anti-CD1d VHH (clone VHH1D22)	Lameris et al., 201641	N/A
Anti-Vγ9 and/or Vδ2 TCR VHH (panel)	de Bruin et al., 201642	N/A
CD1d-Vδ2 bsVHH (clone VHH1D12-VHH5C8)	This paper	N/A
Anti-CD1d VHH WT and variant 1–10 and Q1E (clone VHH1D12)	This paper	N/A
Anti-Vδ2-TCR VHH WT and variant 1–10 (clone VHH5C8)	This paper	N/A
CD1d-Vδ2 hu-bsVHH (LAVA-051)	This paper	N/A
Control gp120-Vδ2 bsVHH (clone VHHL8CJ3-VHH5C8)	This paper	N/A
CD1d-Vγ9 bsTCE (VHH1D22-scFv7A5)	This paper	N/A
Control Vγ9 bsTCE (VHH1D12-scFv7A5)	This paper	N/A
Lymphoprep	Stemcell tenchnologies	Cat# 07861
Critical commercial assays
Counting beads	Thermo Fisher Scientific	Cat# 01-1234-42
BA Human Th1/Th2/Th17 Kit	BD Biosciences	Cat# 560484; RRID:AB_2869353
Annexin V Binding Buffer, 10X concentrate	BD Biosciences	Cat# 556454; RRID:AB_2869074
10X RBC Lysis Buffer	Thermo Fisher Scientific	Cat# 00-4300-54
anti-mous IgG microBeads	Miltenyi	Cat # 130-048-401; RRID:AB_244361
Anti-type 1 NKT microbeads	Miltenyi	Cat # 130-094-842
Anti-PE microbeads	Miltenyi	Cat # 130-048-801; RRID:AB_244373
Pan monocyte isolation kit	Miltenyi	Cat # 130-096-537
Human gamma/delta T cell isolation kit	Stemcell tech	Cat # 19255
Experimental models: Cell lines
Human: CCRF-CEM	ATCC	Cat# CRM-CCL-119; RRID:CVCL_0207
Human: MOLM-13	DSMZ	Cat# ACC-554; RRID:CVCL_2119
Human: NOMO-1	DSMZ	Cat# ACC-542; RRID:CVCL_1609
Human: THP-1	Sigma	Cat# 88081201; RRID:CVCL_0006
Human: MM.1s whether or not expressing mCherry/Luc and/or CD1d)	Lameris et al., 202023	N/A
Human: J.RT3-T3.5 (JRT3) expressing CD1d(sulfatide)-restricted TCR DP10.7	Luoma et al., 201350	N/A
Human: HeLa	M. Kronenberg	N/A
Human: HeLa.CD1d	M. Kronenberg	N/A
Human: A-431	ATCC	Cat# CRL-1555; RRID:CVCL_0037
Human: JY cells	N/A	RRID:CVCL_0108
Experimental models: Organisms/strains
Mouse: NOD scid gamma (AML and MM model)	Charles River	Cat# JAX:005557; RRID:IMSR_JAX:005557
Mouse: NOD scid gamma (T-ALL model)	Vital River laboratories	Cat# JAX:005557; RRID:IMSR_JAX:005557
NHP: M. fascicularis	CrownBio	N/A
Software and algorithms
Kaluza v1.3	Beckman Coulter	https://www.beckman.com/flow-cytometry/software/kaluza; RRID:SCR_016182
FlowJo v10	BD Biosciences	https://www.flowjo.com/; RRID:SCR_008520
FCAP array v3.0	BD Biosciences	https://www.bdbiosciences.com/en-us/products/instruments/software-informatics/instrument-software/fcap-array-software-v3-0.652099w
GraphPad Prism v9.1.0	GraphPad	https://www.graphpad.com/; RRID:SCR_002798
PK Solver software version 2.0	Zhang et al., 201051	N/A