Unfortunately, it doesn't specify (beyond the Fighter Basic Training feat specifying that you count half of your total character level as being fighter levels for the purposes of qualifying for feats, prestige classes, and so on).
Since the book specifies that you can only take the "variant multiclassing feats" for a single class, but does say you can still use traditional multiclassing (i.e. taking levels in other classes when you gain a level), then theoretically there's no reason why you couldn't take levels in (for example) wizard, and also take multiclass feats for cleric so that you can gain enough clerical spellcasting to then take levels in mystic theurge.
Doing so, however, would be less than ideal. In order to take the Cleric Spells II feat (which gives you the ability to cast 3rd-level clerical spells), you need to have taken two prior feats (Cleric Orison and Cleric Spells I) and be at least 11th level (which is one of the prerequisites for Cleric Spells II). Even then, it's questionable if you'd gain new clerical spell slots by taking levels in mystic theurge, as (depending on how literally you want to read it) that prestige class says it grants new spells per day as if you'd gained a level in your spellcasting
class for arcane and divine spells...and your divine spells are coming from a feat rather than a class feature (even if it's modeling a class feature). On the other hand, you could say that since those feats are built around multiclassing into that class, then you would gain more slots and higher-level spells...it's unclear.
I wonder if I should post that in the discussion area on that product's DTRPG sales page?