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CX is used in comparative constructions like the following:
He has more money than I do
Normally an auxiliary like "do" or "have" must be followed by
a participle. In cases like the above, however, this need can
be satisfied by a preceding comparative word like "as" or
"than". Auxiliaries thus carry
do: S- & (I+ or CX-...)
See "MV: Comparatives V".
CX is also used in a few cases of nouns that take relative
clauses consisting only of auxiliaries, like "everything".
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I.p read.v everything I.p could.v
With a cost of 2, we allow auxiliaries to be used without any
participle or complement, under any circumstances. Thus "I do"
and "I could" are accepted.
Grammar Documentation Page.