  The dilaton theorem implies that the contribution to the dilaton potential
from cubic interactions of all levels must be cancelled by the elementary
quartic self-coupling of dilatons. We use this expectation to test the quartic
structure of closed string field theory and to study the rules for level
expansion. We explain how to use the results of Moeller to compute quartic
interactions of states that, just like the dilaton, are neither primary nor
have a simple ghost dependence. Our analysis of cancellations is made richer by
discussing simultaneous dilaton and marginal deformations. We find evidence for
two facts: as the level is increased quartic interactions become suppressed and
closed string field theory may be able to describe arbitrarily large dilaton
deformations.
