user177107 should be commended for asking this clever question.
In short, the described configuration is possible, at least in principle. It will bring two elements into the dynamics.
First, a large moon orbiting a not too large planet may synchronise this planet's rotation. Planet's rotation synchronised with the moon will not be synchronised with the star. As a result of this, the tides in the planet may be contributing either to the tidal ascent or to the tidal descent to the star, dependent on whether the planet's (to be exact, the planet-moon barycentre's) mean motion $n$ is smaller or larger than the planet's spin rate.
[Recall that the tides in a planet whose spin is synchronised with the star are always working to ensure descent, see eqn (150) in this work.]
Second, if the moon is orbiting above the synchronous radius (like Deimos or the Moon), it will usually be ascending. I am saying `usually', because different is a situation where the eccentricity is noticeable. (And it is likely that Phobos was at some point in this exceptional situation -- which helped it to fall down through the synchronous orbit.) Assuming that nothing prevents the orbit from circularisation, and that the moon is ascending, we have to take into account that at some point the moon will be lost to the star. Naively, this should happen when its semimajor axis crosses the Hill radius $r_H$. In reality, the orbit becomes unstable already at $0.49 r_H$, for a prograde-orbiting moon, and $0.93r_H$, for a retrograde-orbiting one. Keep this detail in mind if you decide to integrate this problem.
Foir further reading, this work may be of use.