Probably yes, but more probably, this was a rules blank and you should talk about this with your group to come up with a definite yes or no. The Grab and Escape rules don't prohibit it. Problematically they don't appear to acknowledge the possibility of this either, whilst in the Rules Compendium they've at least created some rules around the case of multiple creatures each grabbing the same one. We've got what we've got though.
Core sources that comment on this are: Player's Handbook (grab p290, escape p288), Rules Compendium (grab and escape p243, the grabbed condition p231), Monster Vault (grabbed condition p307, worth noting for if there's anything specific for monster rules by this point). The RC and MV both talk about the grab occupying the "appendage, object or effect" used to initiate the grab, but "effect" here probably means something physical along the lines of an object or appendage, not that it occupies the power('s effect).
Since each grab costs a standard action, however, doing this would involve using up an action point to make two grabs in one turn. Then you can only sustain the grabs for as long as you keep spending two actions per turn on sustaining them, whilst you can't do anything else.
If your GM has used a monster with a power that could allow it to grab multiple times, it might have specific stuff to say on this topic, and you'd be in the territory of whatever those say.
The mechanics of escape however will differ depending on whether you're using the PHB - the earliest version of the rules - or the RC - the latest version. In both versions, you have to Grab someone first (PHB 290, RC 243) and they have to use the Escape action to break free (PHB 288, RC 243 again) as a move action.
- In the Player's Handbook rules, nobody probably even considered this. No clear word on whether you have to escape each grab individually or can just escape being grabbed altogether.
- In the Rules Compendium, they had considered this. An Escape attempt when "multiple sources" are grabbing you requires just one escape attempt to break free of all of them, but the Escape attempt is harder for each additional source. One person grabbing you twice probably counts as "additional source."
Of course, being teleported out of the grabs or otherwise halting the grabber will end all of them immediately as usual.
This could be a bit of a headache to resolve for the same monster grabbing you twice, so I suggest your group work out how to handle it. I recommend adopting the Rules Compendium's stance and interpreting each grab as another "source."