I would think you would have to call it a new generation every time the yeast goes back into the reproductive part of its life cycle.
Admittedly the amount of yeast that you are effectively pitching when you drop a fresh wort onto a yeast cake is going to be very high. The reproductive phase will be commensurately short (that is until all the dissolved oxygen in the wort is taken up by the yeast and it changes back to anaerobic fermentation).
So the chance that mutated cells will reproduce sufficiently to dramatically change character you expect from that type of yeast is reduced.
Like everything in brewing there are pros and cons:-
Too little yeast and you get a sluggish ferment, some metabolic side-issues produced by the yeast and an increased possibility of other micro flora taking hold.
Too much yeast isnt all good either, as the yeast reproduces it removes some undesirable components from the wort, (like lipids) these are important for the health of the yeast and we want them out of the brew (lipids are head negative and reduce the long-term stability of the beer).
A yeast cake also contains all the dead cells and other detritus that make up the trub, not all of these should be put back into a fresh wort, as they will eventually decompose and taint the beer.
I suppose what I am trying to say is that there is a right amount of yeast.
This is what Stuster is getting with his method, what he has suggested would work well.
There are other possibilities, when I have wanted a lot of fresh yeast I have added 5 Litres of highly aerated wort to the yeast cake, allowed it to start to ferment (goes off like a rocket) after about 6-12 hours, rack into 750 mL bottles with airlocks in them (leaving all the trub that stays on the bottom of the fermenter - on the bottom of the fermenter).
When the ferment is finished just cap the bottles and store in a fridge - you get a 10 or so huge pitches, without all the dead stuff.
The key thing is to not keep making new generations; every generation up's the odds of getting a bad brew.
Try to get as many brews as you can out of the first generation.
MHB