It is definitely possible. I've personally fought 3 at once, then brought a fourth into the battle via powers that shall remain unspoiled.

Dragon are not aggressive enough in my opinion. I am honestly surprised they did not have groups of dragons hunting down our dragonborn, like how the factions in New Vegas sent high level execution squads against the player for angering them.

It JUST happened to me. I was on my way to return the Skeleton Key and two dragons (a Blood and Elder) were fighting some person in a robe. Quite interesting, indeed.

The most I've had is three. One spawned as I was nearing a dragon's lair, where there was one waiting for me, as I ran away in a panic I somehow found myself being accosted by a third one, which promptly ate me.

Fought two dragons, two giants, a mammoth, a cave bear and a sabre cat at once today. There was a lot of monster on monster fighting here.