It varies a lot school to school. MSTP programs are a little different than non MSTP in terms of funding. The non programs can vary a bit. Some schools have set second portal pathways for MD students who become interested, they usually include you having to do research rotations in the summers. Again this varies a lot school to school and the competitiveness of getting a spot varies on how good the applicant pool is year to year. For the most part its not an easy thing to do unless you have a profile that would have made you competitive for entering the program normally.
One person I know of was interested in M1, did a summer research rotation on his own but did not get in, then continued to do some research in the lab over M2 and "applied" again, and got a spot 2/3 through M2, but he did officially go through the interview process like the prospective M1 students. He knew in time to not have to schedule M3 rotations. Another student I know of made her interest known right before M2 and was let into the program at the end of M2 to start her research rotation then but she would have been a strong candidate had she applied the program from the get go. I know of a few other students who interviewed and didn't get into the MSTP but got into the MD, they tried to apply in after doing some summer research but did not get into the program and eventually just went on to M3.