whoa! hold on there big_adventure. now you're talking about stuff that would require artillery and engineers. (seriously, blowing up buildings, taking hostages?)
and THAT sounds more like a USMC division or even
a Task Force than a nuts-and-bolts USMC INFANTRY REGIMENT. a regiment might have roughly 2000 guys in it right now. and before you think that's an unstoppable force... Los Angeles probably has at least five times that many cops that are armed and trained in the use of deadly force. that's not even including all of the other people that would have even more formidable guns but less training. these aren't comic book super soldiers. these are just ordinary people.
if they're really lucky they could copy what Li Mi did after WW2 with his basically 'rogue' 93rd Division. He and his soldiers wandered around Burma for a pretty long time with the aid of the United States... but mostly hijacked the local opium trade and sold that to survive. on top of that the local governments were also trying to suppress numerous rebellions and couldn't throw all of their might against this renegade force. this is about as close to what the OP is thinking of... and even here, they didn't survive without the help of an outside government or two.
https://en.wikipedia.org/wiki/Li_Mi_...China_general)
the OP doesn't stipulate that... so there's not a whole hell of a lot these guys can do in a real-world scenario. most countries that have a regular military can, and would, crush these guys within at least a month or two. ESPECIALLY if they start doing the sorts of things that big_adventure is talking about. that would just get the rogue marines killed even faster.
remember, folks a "medium sized city" anywhere in the world might have 200,000 people in it. that's a numerical advantage of roughly 100-to-1 going against these rogue marines. even if they have superiority in firepower there's simply no way an unsupported regiment can hold out against numerical advantages like that.
my "take over Nauru" scenario doesn't sound that impressive when you compare it to comic book adventure shenanigans... but for a supposedly real-world fighting force with the severe limitations that are implied in the OP that would be a pretty formidable under-taking.