There have definitely been players who've gone back and forth. As long as there's room on the 40-man roster, anyone can spin the roulette wheel! (I think strictly speaking, it's not even necessary to put the player on the 25-man, you could just start a new waiver process - but as a practical matter, perhaps, This Is Just Not Done.)
I doubt it's common, and it may be considered bad form, I don't know, but the Twins and Reds did this dance last year.
Kennys Vargas got waived in March, claimed by the Reds, waived by the Reds two days later, then claimed by the Twins.
The Twins then outrighted him, and the Reds (or anyone else) decided not take another shot. That's when he went to Japan.