How would you go about increasing the buffering capacity of a phosphate buffer?

I know that the answer is that you should increase the concentrations of the acid and base equally or increase the total volume of the buffer solution.

But can someone explain why this works? Thanks.

Sure.

The capacity of a buffer is defined as the amount of acid or base that can be added to the buffer solution without changing the pH more than +/- 1 unit.A buffer, for example, might be composed of
CH3COOH and CH3COONa. I will abbreviate those as HAc and Ac to save time in typing. How do they work? If we add strong acid, such as HCl, to an acetate buffer, the Ac^- takes up the extra H^+ from the HCl to form weak HAc instead of letting it act as a strong acid.
Ac^- + H^+ ==> HAc.
If on the other hand we add a strong base, such as NaOH, the OH^- is taken up by the HAc to form H2O and more Ac^-.
HAc + OH^- ==> H2O + Ac^-

How long do you think you can add strong acid before you've used most of the acetate ion? Probably until perhaps 90% of the Ac^- is used and after that you have no buffer anymore. Or, how much NaOH do you think you can add before most of the HAc has been used? (You can find graphs in most bookis that plot the buffer capacity vs pH). Again, probably 90% of it or so. After that you don't have anymore buffering capacity because almost all of the HAc or Ac^- has been used. So you increase the amount of Ac^- and HAc which is the obvious way of increasing the buffering capacity. More acid lets you "neutralize" more strong base; more base lets you "neutralize" more strong acid. By the way, I don't think increasing the volume of the buffer solution (if you mean simply adding water to increase the volume) will change the buffering capacity. It's moles HAc and moles Ac^- that control how much capacity the buffer has, not the volume. If this is not clear please let me know what you don't understand and why and I'll have another go at it.