Q. Is it permissible to modify the verb tenses in a quotation to fit the grammatical and/or aesthetic structure of a sentence, presuming that the meaning of the original is not otherwise altered?

A. This is not permissible unless you show your changes in brackets:

Sherman asked whether he could alter the verb tenses “presuming that the meaning of the original [was] not otherwise altered.”

You can read about this use of brackets at 13.12 and 13.58. (For other kinds of permitted changes to quotations, see CMOS 13.7–8.)