I wouldn't worry about someone else looking for houses for you - the more the merrier.
What I would be worried about is the joint agreement you both need to make to ensure that in the event of a break up you have both a formal documented record of what you have paid into the house, contents, insurance, maintenance and what you are going to do with each of the assets or proceeds of sale (in what percentage) if you fall out with each other and split up, or if someone else comes in to the house and pays rent??
The early warning signs are already there.