Yes! Any of the round, magnetic badges will fit any of the holders.
I have two mounted on my grill, it's this one: https://www.outmotoring.com/mini-cooper/mini-cooper-grill-badge-holder.html
This one does require removing the grill, but that's pretty easy.
I'm ordering this one for the back: https://www.outmotoring.com/mini-cooper/mini-cooper-double_grill-badge-holder.html
I buy most of my badges from motoringbadges.com or gobadges.com, though I did get a couple from mindthecurve.com