Family Medical Leave Modernization Act This bill amends the Family and Medical Leave Act of 1993 to expand the number of individuals who are permitted to take leave pursuant to that Act. The bill lowers the eligibility theshhold under the Act to any employee who is employed at a worksite at which there are fewer than 15 employees if the total number of employees within 75 miles of such site is fewer than 15. The bill allows an employee to leave under the Act to care for a domestic partner and any individual related by blood or affinity whose close association with the employee is the equivalent of a family relationship if: such an individual has a serious health condition, or because of any qualifying exigency arising out of the fact that such an individual is on covered active duty (or has been notified of an impending call or order to such duty) in the Armed Forces. The bill entitles an employee who is a domestic partner, next of kin of a covered service member, or any individual related by blood or affinity to a covered service member whose close association is the equivalent of a family relationship to leave to care for the service member. The bill entitles employees to specified additional leave to participate in or attend their childrens' and grandchildrens' school or community organization activities, meet routine family medical care needs, or care for their elderly relatives.