The motivation Bill offers seems plausible to me, and quite Neo-Fregean in spirit (which would suit Peacocke).  It is well-known that the
psychological issues concerning Fregean senses come back to haunt the old Fregean in the form of what grasping an abstract third-realm sense
could amount to.  However unpsychological Fregean senses are, it seems inevitable that grasping them (as well as employing them in thought)
would be a psychological relation.  Peacocke may be forestalling the problem by offering a possession-based individuation of concepts, while
still keeping concepts abstract.
    I think Bill is right to raise the question about hyperdyperintensionality - it is something I was wondering about when reading Peacocke.  I don't get the impression he wants to slice concepts as finely as to make FORTNIGHT a different concept from TWO WEEKS, yet by his criterion they should come out different. (The worry was formulated ages ago by Mates, I believe, and has led to all kinds of maneuvers on the part of otherwise good Fregeans.)  I hope we'll get to talk about this at some point.  (Fodor's theory is in part shaped to deal with this problem.)