Maybe she can, but is is implied in the show and even more in the books that dragons form special bond with one human for life. Since dragons live longer it is usually for life of the human, then someone else may ride the dragon again. But it never works like rider changing the dragons or dragon changing riders. Aegon always rode Balerion, and his sisters had their own dragons. There was never mixing of who rides which dragon.
As for Daenerys, dragons love her as their mother. But riding connection was created with Drogon when he saved her from arena. I suppose she will ride only Drogon for as long as she lives.
I'm not sure, but I think in the books Daenerys often contemplates who could be other two riders in order to achive three-headed dragon symbolism. At one point she even thoughthought of marrying both Daario and Jorah, since they are both in love with her and get it over with.