You do not have to refrigerate butter. It is still (just) a solid at room temperature and it’s much easier to mix things into it when it’s in this soft state. It can always be put back in the fridge post-combining and firmed up again. Good old butter.
Nearly anything you might put into mayonnaise, can be mixed into butter. Dry things like spices, very finely chopped/blitzed up herbs, condiments, the list goes on.
I love Tabasco and Lea & Perrins mixed together for toast and crumpets. My girlfriend, Holly Chaves, loves blending anchovies in there. You could buy some Gentleman’s Relish and whack a load of that in. You get the idea.