Let me start from short description of fluorescence (since we talk about it here).
Fluorescence is one of the processes through which excited molecule can relax, lose its excessive energy. That is, quantum interaction between atoms in molecule (organic dye or complex GFP) create permitted energy levels. There is "ground state" $S_0$, for example, and excited state $S_1$. You "pump" your molecule with excitation light from $S_0$ to $S_1$. All this can be nicely illustrated as absorption in Jablonski diagram (look at a for now):
"Loss of energy" here is some process via which molecule returns to ground state. In case of GFP energy is released as an emission photon. Nature of fluorophores is that they tend to return to ground state as the state of less energy, and almost all systems tends to go to state with lesser energy.
Now, to your question. Why GFP can has different excitation profile but same emission? Notice, how in (a) molecule get pumped to highest state, then relaxes a bit to lowest of $S_1$ states and then go all the way to $S_0$? That initial relaxation is thermal relaxation. Some energy is lost, essentially, to water molecules around GFP. That is why emission is always "more red", i.e. has lower energy than excitation. Initial relaxation is why your GFP spectra also broad. There are many levels GFP can emit from, as well as be excited to. In crystals of GFP transitions will be very narrow, because much less of excitation energy will go not into fluorescence.
So, my point is following. Nobody prevents one from engineering a mutant molecule of GFP that could be pumped to some even higher level $S_2$, which then relaxes to $S_1$ via non-irradiative process (e.g. gives energy to water, but not into fluorescence!). Only requirement is that for mutant direct pathway from $S_0$ to $S_1$ would be forbidden (see b and c).
Another point is that whether your spectra are different in shape or only intensity. Different shape of spectra means there are differences in those levels and transitions.