I dont think that you can necessarily bank on improved credit mix resulting in an overall score increase.  Other categories are also affected.

App for a new loan will most likely cause a hard inquiry, which for higher achievers is usually a larger ding. 

Approval will result in reporting of a new account, with an initial age of zero, thus lowering your average age of accounts.

The resulting net effect is questionable.

And, of course, a new installment will result in monthly interest out of pocket.