Can you paint over the covering that a lot of cheaper furniture comes?

For the corner unit, paint using a chalk paint after cleaning well with a degreasing solution. with either wax or a polycrylic product to keep the paint surface. were you wanting to paint the rolltop or keep it natural? My temptation would be to keep it natural, clean it up, do a light sanding to get rid of existing finish and some of the nicks, (re-stain if desired) and put a new finish on it. I would also change up the hardware to give the piece some 'pop'

You might try these steps:

Mix ½ cup trisodium phosphate with one gallon of warm water. Remove any shine or gloss from the surface by sanding it with 120-grit sandpaper. Tape the borders of the trim to protect any area that doesn’t need to be painted. Use a paintbrush to apply a thin coat of primer onto the surface. Apply a coat of gloss paint and let dry. Lightly sand the surface and wipe away the dust. Apply another coat of paint and remove the tape.

Corner unit you can use paint, however you may want to test it first. Sometimes regular paint may not adhere to the surface. I would use a Mineral or Fusion paint. These have a sticking power to them. Chalk paint would work as well.

The roll top can be just refinished with a light sanding and matching varni or can be painted. It's up to you and th look you are trying to achieve. I would also change the hardware into something a little more modern or vintage if that's what you would like the look to go for. Happy Restoration!!

Although I haven't personally tried this, my friend tells me that this primer makes ANYTHING paintable: Rust-Oleum 2004 Zinsser Bulls Eye 1-2-3 White Water-Based Interior/Exterior Primer Sealer, 1-Quart ($8.10 on Amazon.com). Good luck! Let us know how it comes out.

Chalk paint would work. Also an alkyd paint would work.