As identified by the grammarian's group, the following phenomena cannot be given well-formed MRSs compositionally.
ERG: Kim can and should sing. 'Can' and 'should' each have a hole, but 'sing' only has one handle. Rather have the conjoined event 'can and should' related to the handle of 'sing' through an arg_rel.
NorSource: John didn't catch and fry anything
?? Amerindian languages: This approach might give us a handle on attaching syntactically independent modifiers of arguments (noun, pronoun) incorporated into verbs.