This invention provides a cell growth medium comprising (a) a human platelet lysate free of solid matter greater than 0.22 μm in diameter, wherein the lysate constitutes from 2% to 15% of the total volume of the cell growth medium; (b) a human fresh frozen plasma (FFP) filtrate free of solid matter greater than 0.22 μm in diameter, wherein the FFP filtrate constitutes from 1% to 10% of the total volume of the cell growth medium; (c) heparin at a concentration of from 0 U/ml to 10 U/ml of the cell growth medium; (d) L-glutamine at a concentration of from 0.5 mM to 10 mM; and (e) a serum-free, low glucose medium suitable for mammalian cell growth, wherein the serum-free, low glucose medium constitutes from 75% to 97% of the total volume of the cell growth medium, and may contain the L-glutamine of part (d); wherein the cell growth medium permits the expansion of human CD34− stem cells and wherein the resulting expanded CD34− stem cells retain the ability to differentiate. This invention also provides related cell growth medium supplements, a sterile human platelet lysate and human fresh frozen plasma (FFP) filtrate, kits, CD34− stem cell-containing compositions, and related production and cell expansion methods.