Short answer: Yes, if the employer is covered, the employee is eligible and the condition is a serious health condition. The employer can designate the STD absence as FMLA leave so both run at the same time, using up the employee’s 12 workweeks.
Under 29 CFR 825.207(d), leave taken under a disability leave plan counts as FMLA leave for a serious health condition when it meets the FMLA criteria, and the employer may designate it and count it against the employee’s entitlement. The FMLA entitlement is 12 workweeks in a 12-month period (825.200).
FMLA covers employers with 50 or more employees for each working day in 20 or more calendar workweeks in the current or preceding year (825.104). An employee is eligible after 12 months of employment and at least 1,250 hours of service in the previous 12 months (29 U.S.C. 2611(2)). STD itself only replaces income; the FMLA provides the job protection and the right to keep health coverage.
If the employer does not designate, the employee may be able to take 12 more weeks after STD ends. Employers should send the designation notice promptly when an STD claim opens.