Is there a travel agent out there who can clarify what "transfers" means?

Specifically, the rules on a fare read
"4 TRANSFERS PERMITTED. -SURFACE SEGMENTS NOT PERMITTED."

The other relevant part is "NO ENROUTE STOPOVERS PERMITTED. A STOPOVER OCCURS WHEN THE PASSENGER DOES NOT DEPART AN INTERMEDIATE POINT WITHIN 4 HOURS."

Given these rules, what limitations do I have when I choose to beef up a flight with additional segments?

Thanks in advance for your help!