As long as the number of
vehicles is less than or equal to the drivers in your household then it should
be fine to deduct the mileage for more than one vehicle.
Based on the IRS Publication 521 Moving Expenses, you can deduct
either standard mileage ($0.19 per mile) or actual expenses for travel by car
when moving.
I did not find any restrictions regarding the number of vehicles
that you can drive to your new location and be able to deduct the mileage. However, there is a restriction based on the
number of trips and number of members of your household. So, if the number of vehicles is less than or
equal to the number of drivers in your household then the miles should be
deductible.
Here is a link to the IRS Publication 521 for your reference: https://www.irs.gov/pub/irs-pdf/p521.pdf
