In theory, yes. Phased arrays can steer as many independent beams as the connected electronics support. I real life, it's probably going to be dozens or maybe hundreds of beams.
I guess the narrow beam, covers quite a bit of area on earth.
I guess the "narrow" in the current context is the beam widening to hundreds of miles on earth.
IIRC the current Starlink beams are of order 10 miles on the ground. So much narrower than you guess.