TOGA
1. TOGA time limits: engines do not immmediately go BOOM if you would not heed the TOGA time limit. How would an engine know whether to blow after 5 minutes or 10 minutes (the applicable time limit depending on having an engine failure or not).
Thrust higher than Max Continous is time limited because of engine long term life considerations.
MCT is not time limited (what's in a name), but it's use may be restricted by other considerations.
Even lower limits may be set in place for other phases of flight (CLB for climbs, CRZ for use in cruise).
2. TOGA thrust can be obtained at any time by pushing the thrust levers all the way forward to the stop. The little lines along the EPR or N1 gauges that indicate lower limits like CRZ, CLB or MCT are not physical limits for thrust generation, only the orange tic marks are.
The "lower than TOGA limits" are limits to the auto thrust system, ignoring those limits can only be done by physically pushing the thrust levers farther forward.
3. On take-off, heeding the time limit means, selecting another thrust limit (CLB) before the time limit has expired. Formally speaking, it doesn't matter whether actual take-off thrust is only as high as the climb thrust number (as can easily be the case with high assumed temperatures).I
f T/O thrust would be 1.42 EPR and CLB thrust, after selecting it would als be 1.42, still it would constitute a bust of limits to leave thrust in T/O mode for 15 minutes.
Above points only to explain the technicalities. In practice of course, always respect limits as given in FCOM and OPS manuals.
Time limits "in between" applications, well, how do you envision that? A take-off is made once in a flight, how do you want to repeat a T/O a very short time after the first one? The closest approximation would be a flight of circuit training, where the limit mode would almost constantly be GA, do to flaps being extended all the way around the pattern, but surely actual thrust would be very far below the limit most of the time.
And in case you want to practice stalls, sure you would use full thrust for the recovery, but even heavy civil airliners don't need 10 minutes to accelerate out of a stall back to normal flying speeds.