If my wife is very past due on her student loans, but I am current, should we file jointly or separately to maximize our refund amount?

If you file separate returns YOU  do not get any deduction for the student loan interest you paid since when you file MFS you cannot get any education credits.  If your spouse's refund is going to be offset for delinquent student loans, you may want to file as an injured spouse to protect your portion of the refund you may be getting.

There are other factors to consider:

If you were legally married at the end of 2019 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,400 (+$1300 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately

INJURED SPOUSE

https://ttlc.intuit.com/questions/1910698-how-do-i-file-form-8379-injured-spouse-allocation

You are posting from TurboTax Live, so since you are paying an extra fee for help from a CPA, ask for Live help with your issue.

https://ttlc.intuit.com/questions/4124827-how-do-i-connect-with-a-tax-expert-in-turbotax-live