Generally, you have the same tax deduction opportunities as everyone else; a mortgage, donations to charity, pre-tax contributions to an IRA or workplace plan (401k, etc.) There are whole books about the subject.
Regarding your partner, for federal tax purposes, if your partner is not your legally married spouse or your tax dependent, then the value of benefits provided to them are considered additional taxable income to you, even if you never see the cash. This is called "imputed income." For example, suppose that single medical insurance is $500 per month, with the company picking up $400 and you paying $100, That $100 is a pre-tax deduction. Now suppose family insurance is $1000 per month, with the company picking up $800 and you paying $200. The $400 company share for your partner is considered additional taxable income on your pay and W-2, even though you never see it, and the $100 share you pay for the partner's insurance is deducted from your check after tax, not before. The only way to make this go away is to marry your partner, marriage is a "qualifying event" that allows you to change coverage outside the normal open enrollment period. But even then, you don't get the tax advantage retroactive to the beginning of the year, only from the date of the marriage going forward.
In states that recognize a special status for domestic partners, you would have to research whether there is an adjustment or deduction allowed for the cost of company-provided benefits. It would be part of the state-specific adjustments in Turbotax, if it was there.
