If you put (3) of those units in a balanced configuration on a 208Y/120V system, then at full load each line current will be 32A * sqrt(3) = 55.4A. EVSEs require a 125% continuous use factor, so that makes it 69.3A per balanced triple.
Thus a 70A panel could support 3; a 150A panel could support 6; and a 225A panel could support 9, if they are the only loads. Etc.
If you have, say a 400A panel, then you could support 5 triples at 346.5A. The remaining capacity of 53.5A is greater than 40A (32A * 125%), so you could put one more on the panel on any phase. [And actually, you wouldn't quite need 40A of remaining capacity to add an extra, due to the vector addition.]
Cheers, Wayne