Counting data from multiple columns without duplicating if data is in the same row

Hi,

I'm wanting to know how many "clients" are in each "category or combination of categories" (signed, sent, prospective). Each column represents the number of contracts/services for each client. It doesn't matter the number, just as long as it's not 0. How do I count "signed" & "sent" without duplicating the count if a client has signed 1 contract, but has another sent?

Book.xlsx