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A Montagovian verb chomps through a set menu of arguments in a set order. Neo-Davidsonian verbs eat a la carte, selecting variable numbers of modifiers in any order.� Both have drawbacks. For example, the analysis of adjuncts in Montague Grammar is arguably non-compositional. Take the sentences ``Brutus stabbed Caesar'' and ``Brutus stabbed Caesar in the back'': the natural Montagovian analysis would involve two different verbal predicates of different types, though related using a meaning postulate. It cuts against the compositional grain to choose the meaning of the verb according to what else is in the sentence.
Neo-Davidsonian semantics allows just one verbal meaning to be used in such cases, but has other drawbacks. Amongst other things, it greatly complicates the analysis of quantified arguments, and places great demands on the ontology of events.� But existing neo-Montagovian and neo-Davidsonian approaches do not exhaust the space of possible analyses of modification. I offer an alternative.