Yes you can and here is the sizing information.
The front to back dimension is limited but the urine bottle and a small step in the plastic at the bottom. This measures just about 9".
The side to side is limited but the two handle recesses down at the bottom. This also measures about 9"
The height of the bin is limited by the bowl and measures about 7.5"
The ideal bucket dimensions is 9" by 9" by 7.5" or smaller. We have not found one that fits great unfortunately or we would have included it so if you do, please let us know! We will likely develop one in the future but the high costs of molding and time it takes limited us to a back clip design to start.