The latest chart of large Solar System objects lists one (1) Near Earth asteroid greater than Phobos: 1036 Ganymed. It's an Amor, which means it less "Nears Earth" than Nears Mars, as in it crosses that one's orbit. Next biggest is the famous Eros, also Amor, in size between Phobos and Deimos.
We could move these to some Libration halo of Earth or Venus. Eventually though, Earth is doomed, and I'd as soon dismantle it when it finally boils over. In the meantime Earthlings get sore when you move asteroids into their path. And the delta-V would be less for Amor-to-Mars.
Might even dig up some boulders from the far side of our own Moon, to fire out there. I don't think the necessary mass would reduce the Moon's total mass, or orbit, sufficiently for anyone to notice, here or there. Pay it back, if you must, by landing Phoebe on the Moon.
As mentioned I want a bigger Phobos over 15 E, something I can librate more stations around.
I wonder what delta-V would push either of these Amors for a capture by Mars. Better: a trajectory to loop around Mars to hit Phobos, both times from below. First to get it into a Hohmann with mamerostationary; then roll it into that higher orbit.
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