When we got the MS461 last year, I bought a set of AM dogs on eBay for it, similar to the Pro Safety dogs from Bailey's. They never seemed to line up just right, even had to bore the chain catcher hole bigger to fit. I got tired of the aggravation and got our local dealer to order me a set from Stihl. They work great and were about 1/2 the price of Pro Safety dogs.
They didn’t line up because the 046/460/461 case is different than the 044 through 661 and the AM companies don’t really care about that. Your old dogs will fit every other big saw in the lineup (other than the 880 size saws)
I put a big set of cheapo Chinese aftermarket ones on my MS660 6 or 7 years ago. Keeps the wood just a bit farther from the exhaust. I have smoked some dry oak bark on some long cuts in the summer