What you can do depends on the instrument you've employed. If this is done along the lines of the conflict of interest attached to the Standing Orders, I think it has to be related to formal parliamentary functions, which as you recognize is only a limited subset of an MP's contact with other MPs.
My initial concern, using that approach, is that you may only cover a subset of possible interactions. Parliament can legislate anything it likes so it may be you need to go to a legislated authority for an expanded range. The trouble is where you break that off. You have the House of Commons functions and there are party functions as well, which are in a sense meshed in by independent, and then there's a whole range of civic and private relationships as well. It may be that you can only easily control one subset at this stage. The caveat to that is that the House can remove a member for any reason for anything done in their private life. If you are found beating your spouse, and so on, the House can remove you for that private behaviour as rendering you unfit. Working backwards, one should be able to say, if this will render you unfit we can regulate it.