That would be diluting, not strengthening. Strong reputation is where all the links say the same thing. If they say different things, it weakens the original reputation in return for, equally weak, reputation on the additional terms.

But there isn’t anything inherently wrong with ‘weak’ reputation, just as a slow runner can win a race if only slower runners show up, a weak reputation might be enough if the other pages are weaker still.

Use optilink to measure the number and quality of links for the top pages, account for the other factors like page title and page rank, and make a decision. Often, you will find that additional pages focused on your additional terms is a better solution, but not always.