Consider the case of an infinitely thin slit. The resulting diffraction pattern is a cosine squared pattern, thus there is no theoretical limit on the number of maxima you have, it is just a matter of making your aperture/wavelength ratio small enough to acheive a desired number of maxima.
There are, however practical limits. To illuminate the ideal cosine squared diffraction pattern for an infinitely thin slit, you have to contend with the fact that a) The slit is infinitely thin and thus only an infintesimal amount of light will pass through, and b) It would take an infinite amount of power to properly illuminate the pattern anyway.
In practise, the number of maxima you can observe depends on the upper limit of (transmitted power)*(wavelength), this will inturn determine the minimum aperture size and thus the maximum number of maxima you can observe. Obtaining actual figures will require a bit of research and a few elemantary calculations obviously.