Yes.
You can see all their on-page SEO by simply looking at their website.
You can download their backlinks using Ahrefs or MajesticSEO and find out their linking patterns. Most important part in to analyse backlinks that go to their backlinks so you can get the whole structure.
You can analyse their social metrics (retweets, facebook likes, etc) with Ahrefs or SEOMoz tools.
Do it with top 3 ranking sites and look for common patterns. Then, try to replicate it and see if your ranking moves up.
Also, when you look at top 3, keep in mind that besides commons patterns you are looking for something that keeps #2 on top of #3 and #1 on top of #2. In other words, what specifically #1 is doing (or happen to have) that #2 doesn't that makes them rank higher.