To explain a little more, I want to be able manually set off the flash more than once for the purpose of having a double exposure while shooting in manual exposure mode. Is there a way to do this using the Canon XSi that doesn't involve any extra equipment and only the on-camera flash?
Since you're looking to do this with the built-in flash, the answer is a simple "no, sorry". Some other Canon models can use custom firmware which might be able to enable what you want, but not this one.
I would suggest getting a very cheap manual flash which you can trigger by hand, if timing isn't vital. Or, at a higher cost, many non-manual hot-shoe flashes (both from Canon and third-party) have a stroboscopic mode, which does exactly what you want automatically.