Deimos is the kind of place we talk "semimajor" rather than, like dangerous Phobos, "altitude". Once it gets mamerostationary down to 20428 km semimajor, it needs to stay there.
Also, there's much room to boost this moon's mass. If we're also parking Libration satellites in the vicinity: I reckoned last year up to 2.56 × 1022 kg; so, Tritonlike. Deimos is nowhere near this; even Phobos (seven times heavier) isn't near this. The following applies whether that mass at 20428 km is still mostly Deimian or has been overtaken by Phobos material, however that has been done.
As Deimos pulls more mass from below, even if just from Phobos which is as noted starts over seven times Deimos' mass, eventually it will fall below the ideal (stationary) orbit. Conservation of momentum suggests to take on additional momentum from outside Mars' 1.52 AU.
Deimos (and Mars generally) is sited well to take on material from the asteroids. Some of these rocks are considered "Near Earth"; those as don't cross Earth's orbit are "Amors". Eros at 1.4579 AU is the ultra Amor. So we're looking beyond 1.52 AU.
Beyond Mars, the Belt happens to have subsections, delimited by Kirkwood back in the mid 1800s. Among those gaps are 5:1 and 4:1 resonance with Jupiter. That's 1.78 and 2.065 AU from the Sun. Mars has ensured the rocks here don't cross that orbit so - low eccentricity. The asteroids 1.78 - 2.065 AU are the Hungaria group; they trend 16-34° inclination.
Deimos should call dibs on the Hungariae.
Ganymed-no-E is a problem. 2.66 AU but perihelion 1.24 AU. It might actually strike this system one day. The Beltalowda need to fix this.
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