If multiple clients are distributed across multiple APs, (and there is capacity to the WAN, or you are pulling from a local fileserver, squid cache, etc.) then yes, you can potentially move more data than with a single AP.
This is actually a pretty normal mode of "enterprise" WiFi.
However, there are multiple ways to screw it up, and people do that all the time.
One example - in 2.4 GHz space there are but three non-overlapping 20 MHz channels in most of the world - 1, 6 and 11. Gilbert and Sullivan should be called back from the grave to write a song about how 11 channels are but 3 useful channels.
There are NO non-overlapping 40 MHz channels on 2.4 GHz, so don't use 40 MHz channels on 2.4 GHz if you have outside signal or more than one AP. If you are well away from other signal and have just two APs, you COULD set one to 40 MHz, but you have to make sure to set the other one to the channel that's not being used - and the 40 MHz will normally only tell you the "main" channel, and possibly "+/upper" or "-/lower." Few 2.4 GHz client devices work well with 40 MHz anyway - especially Apple ones - if you want that, use 5 GHz.
It is best to keep the APs well-separated, physically. Let each have its area.
Now, the really, Really, REALLY difficult concept for most people - More Power Is Not Always (or even Often) Better. Especially with multiple APs. Crank the power down, way down, for best results.
If you can grasp those, you might succeed. If not, you'll be all too normal.
Clients usually choose strongest signal or best signal to noise ratio. Some clients cling to the AP they first connected to on that basis for an irrationally long time. That can be helped by keeping the APs separated and at low power - it can also be tweaked by kicking the client device into airplane mode for a few seconds.