Is it appropriate to have multiple recommendation letters for an application? I'm currently enrolled in a university program and looking to switch. I know the program I'm looking to switch into is notoriously competitive, and I'm looking to improve my chances in any way I can. I have a few profs who I know quite well and I think would write good letters of recommendation for me. That being said, is it appropriate to submit multiple letters of recommendation? 

My inclination to submit so much more than is required is because the application process caters to high school students rather than university students, on top of the already competitive nature of applications.

A letter of recommendation is not required for the application, but I know it will improve my standing significantly. So I assumed having multiple really good ones would put me even higher up. On the other hand, it could also seem like I'm reaching for praise, especially when no letter of recommendation is technically required. I may be completely misinterpreting the purpose of a reference letter.

In addition to that, if the answer to the above question is that only one letter of recommendation is necessary at most, then is it ethical to ask multiple profs to write letters anyways and then choose the "best one"? My gut reaction is that this is very unethical, as it is wasting the time of the profs, especially after reading this question, but I thought I'd ask it in this context anyways since it might be slightly different.
You should submit what is asked and nothing more.  If they ask for 3 LORs, submit 3, not 5 or 7.  If they don't want any at all, don't waste everyone's time submitting any.