The SW1000XG/MU100/R has 7x 24-bit FX processors, where you can have up to 7 effects set at one time per channel (as long as I'm reading the manual correctly).
Yeah, the manual is kind of deceiving, in my opinion. (Part EQ and System EQ each count as an effect...
The output-routing diagrams in the manual provide the best visual representation of what your options are. In addition to chorus/reverb (the send levels for which are adjustable, per part), and the EQ, you have three assignable multi-effects - Insertion1, Insertion2 and Variation. The insertion effects can only be applied to a single part (at a time), but the variation effect can be applied either to a single part, or to all parts.
So, you're not going to be assigning multi-effects to every part (or even eight, for that matter), but since they can be reassigned on-the-fly, you shouldn't have any trouble making nice, effect-laden music.