Hi Michael,
The bModelTest site model (from the bModelTest package in BEAST) allows averaging over substitution models — so, it won’t recommend model 123323, but possibly sample that model more often than others if that model is well supported by the data.
If you use jModelTest — a program separate from BEAST — it can recommend 123323 as the best fitting model. You can create this model by selecting GTR as substitution model and link the appropriate parameters (after you select the menu Mode/Allow parameter linking in BEAUti 2).
Cheers,
Remco