charles cashion wrote:
All of the door knobs in house are brand Dexter. The knobs are
approaching 25 years old. They are all mounted in 1 7/8" holes.

Q1: Are there other door knob manufacturers that make 1 7/8" hardware?
If the answer is NO, then I must enlarge my present holes
to 2 1/8".

Q2: How can I hold a hole saw steady and centered while it is
enlarging a 1 7/8" hole to 2 1/8" ?
Thank you,
Charles

Don't use a hole saw, use a router with a template, 2 1/8 hole in template.

- OR -

Don't use a template, use a relatively short router bit with a diameter
greater than the shank...extend bit so it doesn't cut all the way through,
use shank to guide on existing hole. Flip work over and repeat. Continue
doing that until the enlarged side of hole is desired diameter then trim
other side with a bit that has a cutting diameter same as the shank.

dadiOH