John Willis wrote:

Why use multiple coats of primer? To fill imperfections in the
surface. Primer is easier to sand and dries fast, thus multiple coats
are easy to put on, sand, and clean up.

One coat of primer will seal the surface, more or less. Multiple
coats, with light sanding and good cleaning between coats, will
provide a very smooth surface and give higher quality results in the
final finish.

The primer is the bonding/sealing coat, or in your case, coats. The
finish paint is the wear and cosmetic coats. As long as there is an
equal amount of finish paint applied, I see no harm in applying more
primer coats. It just seems like it would take more time as you can't
skip the finish coats.

Primer is cheaper than finish paint, and for a good reason. It has
little of the more expensive ingredients that give finish paint its
durability and hiding power (resins and tints).

Sometimes someone will tell me about their miraculous way of tinting a
primer so they can get by with only one coat of finish paint on the
walls. Ain't happening. I want the longevity of at least two finish
coats and that's what I'm willing to pay for.

R