Note that there is a maximum speed rating for each chuck -- and the larger the chuck, the lower that speed rating. At higher speeds, centrifugal stresses can cause the chuck to turn into a collection of Shrapnel flying in different directions.
Now -- if you have collets for the large lathe, you could probably get away with speeding it up. But then you need to worry about other workers not knowing about the speed limitations of the chucks, and/or being too lazy to pull the chuck off and replace it with a much smaller one, or a collet prior to running some high-speed cutting.
Maybe a smaller motor and spindle held in the big chuck could give you high speed when you need it.
Well ... lots of possible ways to do it. One would be a spindle which passes though the main spindle and is held in the large chuck. That one would be driven by an outboard motor which couples in through the back of the spindle.
Another would be a spindle (and bearings) held in the big chuck with a pulley on the workpiece side of the big chuck, and with a belt going to a motor behind the bed -- and likely behind the headstock as well.
In any case, you want to lock the spindle by engaging both back gears and direct drive (unless this is purely gears inside the headstock, in which case I would look for some form of spindle lock on the headstock. And interlock it so nobody can power up the main spindle, because that would beat the motor and the bed to death.
Without seeing the lathe, I don't know what would work best -- and it would also be dependent on what parts you could find. For a really small setup, something like the spindle cartridge from a Unimat SL-1000 (goes for insane prices these days, because they are collector's items). For that, you would have to make a drive tube which threads onto the outside end of the Unmat spindle cartridge in place of the pulley and nut, and extends outside the far end of the main spindle. Install a bearing on the outboard end of the drive tube which is a nice fit inside the outboard end of the big spindle. This would then let you use some small three and four jaw chucks, and with creative work and the WW (watchmaker's) spindle for the Unimat, even really tiny collets.
I wonder whether you could take the spindle cartridge out of a Taig lathe -- a little bigger than a Unimat SL-1000, and a lot more affordable, since it hasn't become a "Collector's Item".
What you would lose would be any existing power feeds on the lathe, and have to come up with some other way to do those, too.
Maybe mount a small cross-slide and compound on the big one, to give you finer feeds.
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