Honestly? I don't think the game engine has the precision to store the amount of experience that you would need to get to level 9999, but if you're adamant about trying, you'll need to find or write a script for it.
But to be completely honest, that only works for NIS because it's 'their thing', because it's never necessary to be anywhere near level 9999 to beat the game (in fact, 100 or lower will generally suffice), and because the really challenging yet conveniently set up places allow you to get a few hundred levels at a time, and I'm not so sure the game engine can handle that either.
Surely it is possible. The engine will have no problem at all maintain the experience as Fixnums will automatically be extended into Bignums (and vice-versa). This means that while there is a limit there are no practical limit. You would be unable to display all the digits on the screen before having problems.
The problem is more that the display is not made for 4 digits levels and that the editor has a fixed limit of 99 levels. The exp curve is based on a formula making it easy to extend to 9999 levels. The problem resides more in the actor parameters (MaxHP, MaxSP, STR, DEX, AGI, INT) They are specified exactly and therefore not generated by a formula. Either you have to create formulas yourself or you have to specify the exact values for the levels 100-9999 for each of the parameters of each of the actors able to be level 9999. (Which is all in Disgaea) In short: It is possible, but there is a lot of practical work in it
I'm assuming that "Bignum" is slang for floating point, but it made me laugh anyway. If Mr. Reaper is, in fact, correct, then as long as you aren't extremely overzealous with your experience totals then you should be fine, but you'll have to rely much more on scripting than most people.
Also, I decided against the "Don't call me Shirley" joke. You really should thank me for that.
Bignum is not at all a slang for floating point. A bignum is still an integer. Here is what the help file tell you about bignums:
The class for long integers, limited only by memory size. The result of an operation is automatically converted into a Fixnum if its value is within range; conversely, if the value is out of Fixnum range, it is extended into a Bignum. For bit operations, Bignum can be considered to be an infinite 2's complement bit string. Negative numbers in particular can operate as a string of 1 bits extending indefinitely to the left. Mixing Bignum with Float can result in digit cancellation errors upon conversion.