When your toolbox is too heavy to carry this project is an alternative to buying a large tool box with casters. That new tool box will probably cost hundreds, but you can make a cart for next to nothing.
Step 1: Measure and Draw
Measure your tool box's foot print and figure out how big the base should be. Leave 6 or 12" extra so you have somewhere to put things down when you're looking around in the box.
Figure out how tall you want the top of the tool box to be by standing next to your tape. Or you may want to determine how tall the base of the box should be, if the work area is more important to you than whatever you keep in the top of your tool box.
I used re-claimed birch-vaneered 1/4" plywood and (mostly reclaimed) 2x4 lumber sawed in half. So not only was the project cheap, it helped me clean out my garage. You can use 2x2 lumber or whatever you have handy. I suggest you take whatever looks right and use something about half as thick. It's amazing how reasonable 2x4 lumber seems when you're drawing something on paper. But be reasonable. A 2x2 frame is really strong---enough for any tool box I've seen.
Step 2: Collect the parts
After drawing your plan, cut out all of the lumber and find the fasteners and tools you expect to use. I've found that this accounts for the majority of the work in any given project.
Step 3: Assembly of back panel
Assemble the back part of the frame. It's 1-1/2" x 1-1/2" lumber, which looks thin, but is very strong. The joints of structures are normally weak points, so instead of worrying about how to strengthen the corners of the frame, I used the entire panel as a gusset.
Step 4: Assemble the middle part of the frame
The middle part of the frame is important for holding up the other side of your tool box. And it supports the shelves. Now you can see why the corners of the shelves are notched.