Nominal more in (1) is ambiguous between the well-studied comparative, (today John spoke with more than 3 students) and an additive, henceforth moreadd, (today he spoke with additional students, possibly only 1):
(1) (Yesterday John spoke with 3 students). Today he spoke with more (students)
I show that nominal moreadd, which is expressed by a separate lexical item in many languages, obeys constraints in both the nominal and the verbal domain, and propose that it is an overt realization of a derived additive measure function on eventualities (Krikfa 1998, Schwarzschild 2002, Nakanishi 2007): It indirectly measures the growth and development of the sum of a presupposed and an asserted eventualities by measuring the growth of the set of individuals (in the denotation of nominal predicates), which participate in this summed eventuality, using a homomorphism.
The analysis is extended to verbal moreadd, as in (2):
(2) a. John slept for 2 hours more / b. ran 2 kilometers more / c. danced twice more
I propose that verbal moreadd can denote a derived additive measure function (using a homomorphism from events to e.g. run times, spatial paths), as in (2,b),or a nonderived one, directly measuring the cardinality of events, with no use of a homomorphism, as in (2c).