What KKORO said. The answer is that yes, you can do it. The answer is that no, you shouldn't try to do it by just screwing wheels to it. The wheels have to be placed onto/into some substantive structural element (not a piece of thin plastic casing of soft foam). Some sort of support plate (or support plates: outside and inside, with bolts instead of screws) is what you'd need.
An alternative is to find something that your current case could be put on to wheel it around. A hand truck or dolly of some sort. This might not work for you if your vision is carting it onto and off of busses, trains, etc. But for some scenarios it would work well.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)