Pitching an idea to sell my book to an agency

I have written a book about being an au pair (an international nanny). My aspiration for the book is to reach every girl/boy who would benefit from it. I have self-published it and sell a small amount of books each month, but I know that I am not reaching as many potential au pairs as are out there. For the longest time I had the idea to approach one or all three of the biggest au pair agencies to ask them if they are interested to buy a certain amounts of books for the au pairs in their program (to include the book in their program). I know that they would only do that if there was a benefit for them. The only reason I could think of so far is that they would offer more value with the book, the au pairs would be more prepared for their journey and there would be less uncertainty because I address all possible issues that can potentially occur during the journey. I have also had the idea that if any of the agencies would be interested I could potentially customise the book to their needs/agency.

So my question is: how do I pitch my idea? If the agencies would be interested- to what price would I offer the book (below market price but what would be an appropriate revenue per book)? Could I potentially sell the book to all three agencies (who are in competition) or would that be wrong? Is there anything I need to be careful about when it comes to making a contract?