One addition which is becoming clearer in my mind with time.
Thinking about it more the problem with music which the composer wishes to play at multiple tempos is how to design an app which caters for it in a way that makes it possible for music at different tempos to come back into alignment. (And by the way everything I say from this point presumes there can be no tempo changes in any section where music is playing at different tempos). There are of course simpler scenarios than others - if for example the tempos in two blocks of music were crotchet equals 60 and crotchet equals 90 the music will with the same time signatures come back into alignment quickly. But if the relationship is one where there are no obvious lowest common multiples things get harder. One is then looking down the barrel of having to enter crazy tempo values with many decimal places for things to align - but what if the values are close but not exact? When would it be enough for the app to realise we are saying “I want this bar in this block - and this bar in this block - to become the same point in time”. My suggestion for how to get around this (and now referring back to my suggestion above) - and by the way I have no idea if there are any conventions in how to deal with these kinds of issues - is that there be a way in any app that provided these capabilities to enter a tempo not as a number but as the tempo value of another block multiplied by a fraction (either the user gets to enter a numerator and a denominator or the program works it out when the user says where they want the musics to come back into alignment - or both). And then when the user goes to add a score tempo marking at a point where musics go out of line it automatically enters the nearest whole number needed (presuming that the performers won’t be guessing such tempo markings but using a click track which is more exact to play to).
So if it was the user - or if it was the developer - how does one work out what fraction to enter in order to make one or more blocks of music come back into alignment? The app could help - it could work out the length - lets say for explanation that the calculations are in number of audio samples whether or not audio was in use - in audio samples - from where music diverged to where it was to reunite - in each block - presuming each block had the same tempo and that the samples were worked out from multiplying the beats of the notation - and the app makes the tempo which isn’t a neat number be a neat number times the inverse of the fraction made from the number of samples in each block (the fraction simplified as much as possible). Hope this makes sense.
And then the notation part of the app when it comes to showing it on a score - looks for the points where alignment goes out and then returns (the existence of fractions making that job much easier) and handles those sections appropriately.