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