Roleset overflow.01 Verbnet Class: NONE "be too full":

Roles:

Arg1:container


Arg2:substance

Examples:

person: ns tense: present aspect: ns voice: active form: gerund


container as subject (-)
With newspapers being the largest single component of solid waste in our landfills, and with our country overflowing with trash, all sectors of our society and all types of businesses must become more responsible in our use and disposal of precious natural resources.
Arg1:	our country
REL:	overflowing
Arg2-with:	trash

person: ns tense: past aspect: ns voice: active form: full


substance as subject (-)
Coffee overflowed John's mug.
Arg2:	Coffee
REL:	overflowed
Arg1:	John's mug

Sounds better on a larger scale: "The floodwaters overflowed the river." Even then doesn't sound great, but I know I've encountered this construction before.