Examples with ambiguous quantifier scope with multiple verbs?

I have been trying to understand scope in MRS… and I am continuously getting closer! But some things still elude me.

I finally have wrapped my head around the benefit of the QEQ constraint in the “every nephew of some famous politician runs” example and how it allows for some underspecification while disallowing unacceptable scope resolutions.

However, in conversations with @ebender she told me that the QEQ between the GTOP and the verb “run” allows for the quantifiers in the sentence to “float between” the GTOP and the verb, but because there’s only one verb it’s difficult to understand why we need the GTOP to point to “the” verb.

What I would love is if someone could give me an example where there’s more than one verb in the sentence that motivates the GTOP =q matrix_verb relationship where quantifiers could “float between” the different verbs in an ambiguous way.

Those this example works for you

The MRS started the underspecified graph

The sentence is “Every boy believes he loves a girl.”