No. Commuting is not deductible, even for the self employed (the W-9 is not relevant). But, the factor of "principal place of business" enters the equation. A client's office can be your principal place of business; in which case your mileage is commuting and not deductible. To deduct mileage, your home just needs to your "Principal Place of Business". See reference links below.
If you go to 2 or more job sites in a single day then the 2nd trip is deductible as an employee expense. For example you leave home drive 80 miles to the client's office then drive 10 miles to the 2nd site. At the end of the day you drive 85 miles home. Only the 10 miles between jobs is deductible. The first trip in the morning, from home and the last trip at night back home are considered commuting and are not deductible.
https://www.irs.gov/pub/irs-drop/rr-99-7.pdf
https://www.irs.gov/publications/p463/ch04.html
