In order to search you will need to know a little about the customer. In mysupply the customer matches the clientkey. A clientkey is a mysupply wrapper for an accountdid. To get the clientkey for an accountdid you will want to use the Client API
To see the makeup of the customer do a GET on the customer API where customer=clientkey.
With the customer information you then construct a search request. The key is to limit the values and facets you request to only those that you need. This example demonstrates what a more complex search looks like.