I would start by trying to deduce what type of finish is on the cabinets. Start w/ denatured alcohol, see if the finish gums up. If yes - finish is most likely shellac and your best case scenario. If no - move onto lacquer thinner. If yes - finish is lacquer, not the end of the world, most likely case. If no - move onto xylene. If no go, you've got some type of varnish finish - worst case scenario, most work, least likely for cabinets from the 90's.
Once you've figured out the finish, you know how you can chemically strip it. Shellac/alcohol will be the most easy to work with, varnish/methylene chloride the most annoying and toxic. Despite what others are saying, wood doesn't need to be "bare" for wood to take it. In fact, the practice of wash coating, which many in this very thread often suggest, is not that of laying stain directly onto wood, but rather some type of coat or as is often marketed by deceiving companies as "pre-stain."
Personally, I would "strip" the existing finish - which is most likely lacquer. then I would stain it. Note, you are not trying to remove the existing stain, rather work with it and add to it to get the desired look. After staining, I would refinish, and I would use a shellac.
With that said, my wife - bless her - has jumped into gel staining all our baseboards and much of the wood in our house. Despite my suggestions above, she has done it over lacquer and shellac with great success. Then my suggestion to shellac over and finish the new coat has gone unheard, as she would rather take the advice of some bimbo with a blog rather than her engineer husband who somewhat enjoys, but is a far cry from a professional, wood finishing. My wife - bless her - uses overpriced briwax, which i offered to make her some, but she prefers the $30/can stuff over the same stuff I can make for a fraction of the price. Even buying a cheaper version, which is the same thing, cannot be heard by my wife due to the bimbo with the blog. I even read from the bible of wood finishing itself (flexner's book), and my wife will not leave her pagan rituals.
other options/add ons/other things to consider
1) dye shellac and brush over - i've never done this, but it would be interesting!
2) if lacquer or shellac, make a 1 lb cut of shellac, brush on, then gel stain/normal stain/glaze, then finish coat
3) if oak, and you dislike pores, how will you plan to fill the pores? same goes for any wood with pores
4) do as my wife - bless her - does and just go for it. The worse that will happen is you end up redoing it a couple years later, but who know, maybe light stain will be back in by then. My wife - bless her - does do a light sand coat w/ 320 or 400 grit sandpaper.
so yes, it is possible. A little testing upfront can give huge confidence in its longevity.