The reason I ask is because I really liked this one program that is smaller and less well-known, but when I was interviewing there, they kept saying something to the effect of me not going to rank them high because I probably have much better offers. I guess they just got that impression from looking at my application, but I was wondering if doing a second-look at that program, even if it's me initiating it, would help convince them that I really am planning to rank that program high.
Unfortunately, I'm personally not sure that a second look initiated from you would help. If your intent is to rank them #1, just tell them that. (As an aside although may not be relevant to you: Don't tell a program that you are "ranking them highly" if they are not #1 on their list because this will peeve them off more than anything since they will know that you are not ranking them #1. Programs are quite insecure and don't like to hear that they are not ranked #1. Then again, it would suck if your significant other told you that they were going to rank you #2 on their passion ladder...so maybe it's human nature to dislike not being ranked #1).
Essentially the program is going to wonder if you are going to rank them #1 if you are coming for a second look. Either you: 1) just tell them outright that they are #1, 2) go for a second look and tell them that you will rank them #1 (but then why do the second look anyway), or 3) go for a second look and not tell them that you are ranking them #1 (in which case they will wonder why you came for the second look and didn't rank them #1). A fourth scenario is that you go for the 2nd look and they realize that you are serious but not serious enough to rank them #1 but the program remains satisfied that you consider them highly (not likely that they will feel good about this since derm programs want to be wanted). This in a nutshell is why, unless initiated by the program, a 2nd look is not advantageous.
In the real world, a second look is really valuable and can help both you and the program get to know each other a little better. So, you could gently talk to your advisor (presuming you know him/her well) and see what he/she thinks of the idea, especially if they know anyone within the program. However, if you are going to rank them #1, just let them know that you are ranking them #1.
Are you in the situation where you would love to go there but don't want to rank them #1 either? Sounds like you are but don't want to assume.
As an aside, if an applicant turns down a second look initiated by a program, you can rest assure that the program won't like that either (believe it or not, I've seen it...amazing huh?).
