Satellite array antenna beamforming - basic intuition help
Let's only talk about phased array antennas. 

YES, it's well possible to have different beams for simultaneous signals. But the delay must be adjusted separately for every antenna element and for every signal. In theory it would be even possible to transmit from one array different signals to different directions at the same carrier frequency. That's because in linear signal processing separate signals do not disturb each other. 

I guess making the right phase shift in the baseband separately for every antenna element and for every signal costs money if the array has say 500 elements.  But there are institutions who do not ask the price when something essential is needed, so I do not know do such systems exist.