UNDERLAY

To lay (something) underneath something else; to put under.

To provide a support for something; to raise or support by something laid under.

"to underlay a cut, plate, or the like, for printing"

To put a tap on (a shoe).

To lie in a position directly beneath.

To lie under or beneath.

"A stratum of clay underlies the surface gravel."

To serve as a basis of; form the foundation of.

"a doctrine underlying a theory"