It all depends. For instance if these are rubber tires and you have no outriggers and you don't mind if there is some rotation or tilt angle of the machine on ground that has no give, such as solid concrete. In that case how much can those tires deflect without causing trouble? So how much tilt is OK? What is the spacing of the wheel supports? Is there an occasion where almost all your load can apply to only one tire? So you see there are mechanical calculations you may need to do to show the actual load to each tire that you will apply as well as how much can that loaded area deflect downward and still be acceptable?
If you have some allowable tilt angle under those circumstances, then you provide the geotech some information as to how much that compacted fill can settle. Thus, the allowable bearing capacity that someone may say you need, will depend on the allowable settlement under load.
Do you have adjustment potential for taking up such settlement at each support? Is this just a temporary job thing or a permanent support situation? What tire pressure do you require, since that may be the required bearing capacity of the ground below, as a rough answer.