Here’s yet another issue relating to use of may—the phrase may require.
My principal problem with may require is that in its most common use, it frames as Party X’s discretion what is best thought of as Party Y’s obligation. I recommend that you omit this use of may require in favor of language of obligation:
The Company may require a Participant to retainAt the Company’s written request, a Participant shall retain the shares purchased on that Participant’s behalf in the Participant’s ESPP Broker Account until the sale of such shares. The Bank may also require each Borrower to establishAt the Bank’s written request, each Borrower shall establish a lockbox under the control of Bank to which all applicable Account Debtors shall forward payments on the Accounts.
The other uses of may require? Sometimes the may is used to indicate possibility rather than discretion:
The issuer of these securities may require an opinion of counsel in form and substance satisfactory to the issuer to the effect that any proposed transfer or resale is in compliance with the act and any applicable state securities laws.
In that case, I’d use might rather than may. (See this blog post for more on using may to indicate possibility.)
And the may in may require is also used to convey possibility in a restrictive relative clause modifying a noun phrase:
Borrowers shall complete and sign such applications and supplemental agreements and provide such other documentation as Bank may require in respect to the issuance and administration of the Letters of Credit.
In that context the may is superfluous; use the simple present instead. (For more on this, see MSCD 3.58.)