(usu + off on/on/upon) to force acceptance of (something or somebody unwanted) by somebody, or to force (somebody) to accept something or somebody they do not want

Many constituencies don't like to have someone foisted on them — Jeffrey Archer

(usu + off on/on/upon) to deceitfully pass (something or somebody) off as genuine or worthy

(usu + in/into) to introduce or insert (something) surreptitiously or without warrant