You can make a mortise that is wider accross the grain than along the grain, but I think, it is safer to keep the cutting accross the grain. Along the grain, you are seperating the fibres more than cutting and you cannot predict, how long this separation will continue. Always imagine the wood fibres as a bundle of slightly sticky straws, this helps a lot to figure out, what can happen.
Paul Sellers made a video where he compares a mortise chisel to a “normal” chisel. I think, it is the one, where he explains best, how to cut a mortise efficiently.