We have to clarify what you mean by "support multiple simultaneous beams". The SL receiver is half-duplex, so it can only send or receive at any given time, and, in theory anyway, it uses beamforming to communicate with just one bird at a time (if it couldn't beamform to within sufficient tolerance, then that would be an FCC no-no.) There's no theoretical reason, AFAIK, that it couldn't rapidly switch between birds, but the actual feasibility of that depends on terminal firmware, the ground network being setup to handle that, the arc between two birds, and whether or not the antenna's scan angle can encompass that arc.
The primary difference between the ground terminals and the antennas in space is the amount of power passing through them, but also their sophistication (primarily the beamforming capability.)