Per the BJCP guidelines an American red (referred to as American amber in the guidelines) can be well hopped. American versions of classic styles are generally more hopped and have a cleaner fermentation character. So it would follow that an imperial American red would have high hop bitterness and a pretty significant late hop character, which is typical of most commercial examples of imperial American red.
To answer your question, Gold_Robber, essentially yes. A larger grain bill and a higher hopping rate will accomplish what you desire. One thing to note, however, is that while American reds have a medium-ish body, imperial American reds tend to finish a little higher giving it a little fuller body than the standard version.
EDIT: Just wanted to clarify where I got the info about the imperial red. It comes from the Brewer's Association style guidelines since there is no imperial red style in the BJCP guidelines.