When I first saw this post, I was assuming it was asking about finding an actual LMT who's open to doing a happy ending (or perhaps more...), I hadn't really considered AMPs since I've never really thought of them as "legit" massage. So, if that's more what you're looking for...
Yes, it does happen from time to time. It's not easy to find. I suspect the most reliable way to find such a thing is by personal referral from another "satisfied" client. This may be hard to come by, because a client who's seeing an LMT who's open to extras is probably not going to mention it unless the client is aware that the masseuse is open to doing such things with other clients (like if the masseuse has specifically told the client something like "if you enjoy the service I provide, feel free to refer your friends"), and even then you'll probably only get such a referral from someone who knows you and trusts you, because the client won't want to so anything to potentially mess up their own deal.
Aside from that, the best strategy I can think of is to start seeing an LMT that you might be interested in obtaining such services from, building a relationship with her as a regular, and seeing what happens. In general, if you're seeing an LMT looking for extras, you have to realize that the default answer in most cases is going to be "no" - even if they otherwise wouldn't mind, they can't just come out and offer extras to clients they don't know well and trust, because they'd be at risk of losing their license (and thus not being able to work at legit spas or private practice anywhere in PA). So it's not going to happen unless you're known and trusted (or referred by someone she knows and trusts). You really can't do the typical AMP strategy of "let your hands wander and see what happens" because that's just rude in this scenario, given that most LMTs don't provide any extras - it is likely to just piss her off, and may get you asked to leave. (Honestly, even at an AMP, I personally think this is pretty rude too, but at least girls at AMPs generally expect it and tolerate it to some extent - legit LMTs may sort of "expect" it as well because they know they'll occasionally get clients who try to push boundaries, but they may be a lot less willing to tolerate it...) You just have to be chill, and wait to see if the masseuse will offer it herself.
If you are really hoping for extras from some specific LMT that you don't otherwise have an "in" with, you're probably just going to have to bite the bullet and invest in a few sessions over a period of a couple of months just to build up trust. Then on maybe the third or fourth visit, wait until she has you flip over, then just lay back, relax, and let yourself get an erection. Worst case, the masseuse will just ignore it (as legit masseuses are generally trained to do); if it's raised as a topic of conversation, you have the plausible deniability of just saying something like, "Sorry, I'm just so comfortable with you that I guess it's developed a mind of it's own", or something like that. Best case, she may offer "I can do something about that for you, if you like", or some such... But it totally needs to be her own idea.
If that doesn't produce any results, probably the best strategy is to move on and try again with a different masseuse, walking away with the consolation prize that at least you probably got some decent massages.
Or, you could just go to an AMP ... since trying to do this with a legit LMT is a shot in the dark that is much less likely to produce the desired outcome than not.