Potentially, yes. If your work assignment is for a period of one-year or less, then you haven't changed what is known as your "tax home." If your work assignment is for over one-year, in the same location, then your tax home will have changed. In that instance, the airfare expense for traveling back and forth, from wherever you do, could not be tax deductible, unless the travel was for the purpose of actual work, such as visiting another work site or company headquarters. For more details, please refer to IRS Publication 463, starting at Chapter 1. Here is a link:
https://www.irs.gov/pub/irs-pdf/p463.pdf
Now then, let's assume that your work assignment is for less than a year, and your tax home therefore hasn't changed. To the extent that your company's travel reimbursement(s) don't cover the full cost of your travel, then you can take that excess amount you paid as an "Unreimbursed Employee Business Expense." The further catch is that such expenses are subject to a 2% rule, based on your "Adjusted Gross Income." Moreover, you will only benefit from such a deduction if you itemize your deductions, in lieu of taking the standard deduction, as the majority of taxpayers do. The following TurboTax page will explain this in more detail:
https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Deductions-and-Credits/Employees-Can-Deduct-Workp...
Hopefully this answer, and the linked information, will provide you with enough information to determine your own answer, based on your unique circumstances. Remember, however, that even if you can "deduct" the travel costs, unless you can further meet the hurdles described above, the "deduction" may not actually benefit you.
All it costs you to find out, however, is your own time. TurboTax will take care of all the calculations and tax forms, after you input your expense data.
