If I use multiple wifi base stations on the same network will that improve the transfer speeds over just having the one.
You mean you're just seeing slowdown and what you're doing isn't typical network use? No. Your laptop will still only be talking to one base station at once.
Now if you actually mean "I have 60 machines connected to one station and we're all downloading files while watching netflix because that's just how we roll where I work" then yes, you're overloading the base station and should probably look at your network infrastructure some more (and probably move to wired connections, if that's really what you're doing, real world wireless simply isn't as good as those intel adverts with someone sitting in a field looking like downloading files from the web is the most exciting thing they ever did in their whole life).