To get up to 32mm you need an ER40 collet chuck. ArcEuro have advice about ER32 chuck sizes for various mini-lathes here, and details of their ER40 chucks here. Depending on which mini-lathe you have, the 100mm ER40 might fit, otherwise you'll have to make a backplate.
Are collets essential? The alternative is to get slick with a 4-jaw and DTI. Not as convenient as collets, but they can be set very accurately.
Dave