Shop thrift stores and garage sales for storage ideas--- baskets, CD/Cassette holders, small cabinets, etc.
Depending on the size of the dresser, you could use a flat piece of material as a desk top and make your own pull-out surface. A scrap of countertop or wood would sit atop a pulled out drawer as a work surface. When not in use, lien the piece against the side of the dresser.
I still think "go vertical" is a good option. Stack and build on top of the dresser.
For underneath (depending on the space), maybe an under-the-bed storage container would work. My daughter has one that's wire mesh with wheels.