It has absolutely no advantage whatsoever. This question was asked the open day I went to and the Dr Brenda Cross addressed it herself. So long as you take biology and chemistry and one other subject to A2, it is adequate. If you take 4 or more, they will not care at all - and will not show any sympathy or flexibility if you miss an offer due to taking on extra subjects.
It is to ensure fairness, as lots of schools are very heavy handed in pretty much shoving their kids either to drop a subject or take all 4 forward to A2 and this is rather unfair either way.
The only reason I took 4 was because I got 100% in RS and 95% in Maths, meaning I'd only have to scrape Cs (on average) per module in order to get As in them
which isn't really a lot of effort and I thought I might as well - especially as if I didn't get into medicine - I'd either do a science course (which helps having maths) or go into teaching (either philosophy or politics) after taking a few extra A-levels.
Seriously, don't take 4 unless you really love the subjects. You are at NO ADVANTAGE whatsoever in the admissions process other than you might have the possibility to totally cock up one subject - my offer was AAA (including chemistry, biology) meaning they didn't mind what my 3rd A was in... However, I have heard of some people taking 4+ subjects and they specified what they wanted the 3rd A in as well which could screw you up if you're doing badly in it and think you got the others to fall back on!
And also, the admissions team will definitely not look at things lightly if you apply with 4+ subjects and then get an offer/interview and subsequently decide to drop it (you must inform them as they are entitled to withdraw their offer as it was based on the info of you taking on that many subjects).
But by far, most of the applicants had 3 subjects (both that I met at interview, and on the freshers groups of UCL medics). BMAT prep is definitely the most important thing you should be doing in the 3 weeks leading up to it. If you're really keen you can start a month early, but 3 weeks is plenty of time!