If you want to search for messages across all parties you can represent, you can do so by clicking the blue circle on top of the page and Show all parties. On the right side you will find Search across parties.
From this page you can search across all the parties you can represent.
You can limit the hits by whether you are searching in the inbox, archive or deleted. You can also limit the search to specific statuses, or for a given period. (If you search for messages with the status Unread, and someone else in the organization has opened the message, you will not get any hits)
If you click on parties, you can choose whether you want to search among one or more parties you have access to, including the subunits you have access to.
You'll also be able to save the search, so that you don't have to enter the search information every time you want to make a specific search.