What is the difference?

Hi. I've been playing tenor for about 20 years, and for the last few have been trying to get the altissimo thing going. At this point it's kind of frustrating. I've got a really strong playable F#3 and G3 (although sometimes I have to "grace note" up to the G) both with a good strong sound and good intonation. On a really good day I can play G#3 and A3, and when these are working they sound great, but can't consistantly play them. I work overtones and on these I can get to the second octave, ie Bb, B, and C3 with the low octave fingering, but that's pretty much it. My question is what happens on notes higher than G3 that's significantly different? As I say I've got a good solid dependable G3 and really nothing above that. I'm not looking to give Lenny Pickett a run for his money, but I'd love to have maybe a C or D4 in my toolbox. Thanks!