Most contemporary employers offer some policies to facilitate work-family (WF) balance for their employees. However, do the policies designed to help everyone suffice for unique employees with stigmatized social identities and non-traditional family structures? We conceptualize stigmatized family identity (SFI) to provide key insights on distinct WF issues experienced by such employees, and potential solutions in the form of person-specific work arrangements called idiosyncratic deals (i-deals). First, we define the construct of SFI, and exemplify its different types arising from the intersection of sexual orientation/gender identity/race and a non-traditional family structure. Second, we integrate literatures on WF and stigma to theorize the broad spectrum of WF issues and ensuing effects on job outcomes of employees with SFIs. Finally, we advance theory by developing a multi-level framework highlighting the importance of flexibility i-deals for employees with SFIs. Our framework identifies boundary conditions at individual, team, and organizational levels that can encourage (or deter) such employees from seeking i-deals. In doing so, we also explore the importance of privilege when it comes to SFI employees seeking i-deals.