Personally, I would recommend that you seek professional tax/legal guidance with respect to this transaction. There could be certain gift tax (return filing) issues involved and a professional may be able to provide you with more beneficial options for structuring this arrangement with your son.

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@keatja1 wrote:

My first question is:  Can I declare the mortgage interest on this "third" home?

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You cannot deduct the mortgage interest on a third home; it would not be considered a "qualified home" by the IRS for that purpose.

See https://www.irs.gov/publications/p936#en_US_2018_publink1000229900

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@keatja1 wrote:

My second question is: Since my son is paying some rent, would I consider this an investment property rather than a third home?

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You would not able to consider the home as a rental property (report the income and deduct the mortgage interest paid) since your son is (almost certainly) paying less than fair rental value. As a result, the home is considered to be used by you for personal purposes (per Section 280A).

the home is in my name put the mortgage is in someone else's name. I make the payment

If you are renting the property for less than fair market value, you need to report the rent income as "other income" in TurboTax as follows:

1. Go to the "Federal" section of TurboTax

2. Click on "Income and Expenses"

3. Find "Less Common Income" and choose the last entry "Miscellaneous Income"

4. On the next screen, "Miscellaneous Income" choose the last entry "Other Reportable Income"

5. Enter a description for your entry (Rent), and enter the rent received

You can deduct the property tax on the house in the "Deductions and Credits" section of TurboTax, but you cannot deduct the mortgage interest, since you have three houses. You can enter other expenses of the rental as miscellaneous itemized deductions, but they will not be deductible on your federal tax return in 2019.