God stands alone (and when I say that, I mean the trinitarian Godhead). Nothing else is what he is; nothing else has independent existence as he does; everything else was fashioned by him, yet he was fashioned by nothing. We generally jump immediately to the moral repercussions of God's separateness when speaking of holiness, but to do so is to not go deep enough into the subject.
If we don't plumb far enough, however, we generally devolve into some kind of petty rule keeping regimen in order to give us some sense we're aligned with the command to be holy. Holiness, however, can never arise from that which is intrinsically unholy. So, perhaps we need to rethink the force of the command, and see it more as an invitation. Like any of the commands of God in the old covenant, the point was not to elicit actual obedience, but to make us aware of just how unholy we truly are, and thereby to lead us to the gracious hand of Christ.
Oh, it's not that it's possible to be unholy and get along with with God, it's just that we can't achieve holiness by our own efforts. If we're to be holy, as we must to get into heaven (not to earn it, but just to survive it), holiness has to come to us, imported like oil is to Singapore. Since we must be holy to co-exist with God, we must come to Christ and receive the gift of his nature which alone is holy. When the holy one is in us, holiness becomes possible for us.