under bed sliding containers but I would read the Life Changing Magic of Tidying up. Especially when it's two peoples' worth of stuff to store
+1
Try this book. If you can get past the crazy lady sections, just roll your eyes and move on, the practical advice in this book is pretty amazing.
We recently moved into a home that is a decent size but has a small, oddly shaped master bedroom and tiny closets from the 1940's. My huge dresser didn't fit. His did. So we went through both dressers before we moved, and by weeding out what we actually never wore, and learning to fold properly (upright like a filing cabinet), we got both of us into his. He has 4 drawers, I have 2. He used to have 2 drawers just in t-shirts, but after folding the crazy lady way they all fit into one drawer. It works!
If your SO resists, lead by example. Mine thought I was nuts until he saw all my empty dresser drawers, and then when I refolded his shirts so he could actually see them all in one glance in one drawer, he was hooked.
We also have a box under the dresser that can't be seen that stores misc stuff like belts and thick winter socks, and we have a cloth bin in the coat closet for gloves and scarves.
We didn't have room for drawers underneath the bed because there is only a foot to spare on each side of our bed, so we have a new bedframe that is on hydraulics where the entire mattress lifts up and we can use the space underneath for linens, spare pillows, and misc crap. Huge help. We don't have room for nightstands so we have shelves. Works just fine.