Upgrading battery - how do you know what a controller can handle?

I currently have an E-Lux Tahoe Sport with a 48V/20A battery and I was thinking of picking up a spare battery. In the process, I was considering a 52V/20A since the price difference is negligible. And from what I've seen things can be a little more efficient that way as well - At least I think so? I often run the 48V at close to max power, so if I could run the 52V on slightly lower it'd be into more efficient parts of the power curve - am I correct in my thinking here?

The main question is, how do I know if my controller can handle it if I'm not 100% sure on the specs? Is there a way to easily find out?
 
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