Have a home and a 2nd. Bought a rental. Did not have any income in first year. Am I able to claim any of the 1st years mortgage interest? Perhaps add it to cost basis?

It depends on whether the property was being advertised and available for rent during the first year.  If you were advertising and trying to obtain a renter, then the property is considered to be a rental property regardless of whether you received rental income.  If it is considered a rental property, then your mortgage interest is a rental expense that can be deducted on Schedule E, along with other rental expenses such as property tax, utilities, insurance, etc.

If you did not advertise and make the property available to rent, then you cannot deduct the mortgage interest and it would not be added to the basis.  You also would not be able to deduct the mortgage interest as part of your Schedule A Itemized Deductions since you stated you already own two properties in addition to the rental.