From my research, a suppressor will work best in the maximum caliber it's designed for. It will work for smaller calibers, but not as well. Also, bigger calibers may require a bigger, heavier, suppressor. So, a .308 suppressor will work on a .223, but not as well as a .223 can. The .308 can may also weigh more and be bigger.
I know that Yankee Hill, a large suppressor maker, makes adapters allowing caliber changes, or more accurately, using one can on guns of different caliber. Remember that the barrel outside diameter is what's important, not the size of the hole in it.