A tentative foray into the question:
1. One argument for why Christians can't be possessed is there's no example in the Bible of a demon possessed Christian. Of course, that's an argument from silence at best.
2. To my knowledge, the main argument that Christians can't be possessed is based on the fact that Christians are indwelt by the Holy Spirit, and as those who have the Holy Spirit abiding in them, Christians can't have an unclean spirit like a demonic spirit abiding in them at the same time. Hence, the argument goes, Christians can't be possessed. Supporting verses like 2 Cor 6:15-16, 1 Jn 2:13, 1 Jn 4:4 are cited.
3. However, empirically speaking, I've heard of credible cases about Christians who have been possessed. For example, the evangelical Lutheran pastor-scholar and exorcist Robert Bennett has talked about such cases in various interviews. I don't see any good reason to doubt Bennett at this time, but to be fair one could question the legitimacy of the evidence.
4. That said, assuming the evidence is reliable and credible, if it's true Christians can't be possessed, then the only alternative is that these weren't bona fide Christians in the first place. Yet if a person has a credible profession of faith, has lived a godly life committed to Christ, and so on, then why doubt they were a bona fide Christian in the first place?
Also, if it's possible for Christians to be possessed, but possessed Christians are treated like non-Christians, then that might do a disservice to these Christians. It might make them question their salvation. It might make them despair. Like fighting a two front war: on the one hand possessed by a demon, but on the other hand their profession called into question by fellow Christians as if their faith isn't genuine.
5. What about the argument itself that Christians can't be possessed because Christians are indwelt by the Holy Spirit?
Bennett brings up the point that even as Christians we have a sinful nature. We're still warring against the flesh though the Spirit dwells in us. As such, it's possible for two contrary "natures" (there's got to be a better word or term for this) to co-exist in the same person. Bennett seems to believe this is analogous to an unclean spirit like an evil spirit dwelling in the same person as the Holy Spirit.
However, I don't know if that's necessarily the case. Maybe, maybe not, for it seems to me our sinful nature is still part of our person, unlike an evil spirit which would be a completely separate entity or being.
6. Let's step away from persons. Consider a haunted house. Can a Christian live in a house that's haunted? I don't see why not. If so, then wouldn't the house have the presence of God as well as the presence of an evil spirit within its confines? Of course this is another argument from analogy and it assumes that people are like places or houses. Maybe that's not the case.
7. I suppose all this goes to the question of what it means for the Spirit to dwell in the Christian. What exactly is the indwelling of the Holy Spirit?
I don't see how the Holy Spirit can be physically present in a person, for the Holy Spirit is not physical. Likewise neither is an evil spirit. So it seems to me we can rule out a purely physical sense of dwelling. I think that's fairly obvious.
This doesn't mean a spirit can't interact with material objects including human beings. Hence a relevant question may be the question of how a non-physical spirit interacts with a physical human being.
Is being indwelled by the Spirit synonymous with regeneration? Union with Christ? Is it something else or something more?
