Capacitors in parallel
The charging circuit was designed for one capacitor.  If you put in three more then the charger has to be able to source current for a longer amount of time.

If the charge circuit was overdesigned then it should work just fine!  However, if the designers didn't build in any "wiggle room" then it might overheat and destroy the charge circuitry.

Make sure that all your caps are rated at minimum for the voltage of the original cap.

I would go ahead and try it.  It will likely work, and if it fails then your are only out one disposable camera circuit...

And here is the obligatory warning: Don't mess with high voltage unless you know what you're doing!  These circuits charge to around 300VDC!