Synonyms for Build up:

n.

ply with, lay on, accommodate, nourish, cater, feed, serve, support, house, take in. play up, overstate, inflate, dignify, glorify, overplay, idealize. raise (someone's) hopes/expectations, build up someone's hopes, sustain, embolden, encourage, uplift, hearten. expand, add to, increase. talk up, promote, magnify, advertise, boost, praise, exaggerate. build up (noun)
build, fortify, progress, gird, work up, arm.

v.

amplify, advertise (verb)
boost, expand, increase, fortify, promote, add to.

Other synonyms:

inflate, advertise, expand, magnify. increase. boost. promote. energize
work up.
expand
expand.
overdraw
exaggerate.
praise
glorify.
Other relevant words:
magnify, talk up, overstate, play up, expand, boost, exaggerate, increase, advertise, praise, inflate, add to, promote, glorify.