If you want collets, it might be better to opt for ER collets.
They comne inb a different sizes, from ER16 up to ER40.
ER 20 will accept up to 13 mm, ER25 will accelpt up to 16 mm, ER32 up to 20 mm.
ER, being slit from both ends, have the advantage that each will grip a 1 mm range of sizes (Other than the smaller sizes, 1 – 3 mm, which have a gripping range of 0.5 mm )
Thus they can be used to hold Imperial or Matric stock or cutters.
A collet chuck on a 2 MT arbor does not allow work to pass through into the Spindle bore, but a collet chuck, on a backplate does. (Up to the maximum size that will pass through a 2MT bore.
Howard