APs don’t sign up with multiple agencies because it’s time consuming and eventually expensive. Some do their homework, but most sign up with the most popular agency in their country, or based on a reference from a friend. I suspect CHI, because of its size, uses partners in every country (that’s what InterExchange does).
You can ask an au pair to switch to your agency (only if abroad- can’t do for year2). I have done in 4 times. The amount they pay before matching is minimal, around 100
Euros, so if you are willing to reimburse for that amount, I can’t imagine why an au pair would say no, especially if she really likes your family. You will likely get a discount with the agency for prematching. In one case, we asked a CC au pair to switch and she insisted on us not reimbursing her the registration fee because she said the total cost was still going to be much cheaper for her with the new agency.
Also depending on the agency, they will accept the other agency’s au pair dossier pretty much as is wan a starting point and may settle for a Skype interview instead of in person, since the au pair was already accepted in the program. From my experience, it’s pretty quick.