Hey, you gotta be careful when you ask for "any insight".
The best way to know what
you can put on
your frame is to measure the clearance around the tires you have. I like to use allen wrenches as feeler gauges. Let's say you have 23mm tires on now, and you can slip a 3mm allen wrench in between your front tire and the fork crown. Well, since tires are roughly circular, that means a 25mm tire would be about 2mm taller, and an extra mm on each side. Probably not enough clearance for a 28mm in this example though. Rear tire is much the same, except you have to keep an eye on the chainstay clearance too.
Unless there is an NJS/keirin spec for tire clearance, it's very possible for two track bikes to have different tire clearances, so the size of tires someone else can fit may not be applicable to you...