A company representative reported an aircraft issued taxi instructions to the FBO had to stop at an intersection to avoid two other aircraft taxiing through the intersection.

Narrative

PIC Report. 'After landing on runway XX; the crew were instructed to exit the runway via [taxiway] 1 then to taxi straight ahead [taxiway] 2 to the FBO and to stay with him on his frequency (no change to ground). The crew proceeded to exit via 1 and slowly towards 2. Just after passing the runway hold line; the crew saw a Challenger Jet taxiing on 3 from left to right. The crew saw the traffic just in time and stopped immediately to let the aircraft pass. There was a second aircraft; Global; right behind that also proceeded left to right on 3. We notified the tower immediately of the 2 passing aircraft to confirm that we were still good to proceed. The tower simply clarified the same original taxi instructions and did not seem to understand what had just happened. The PM; advised the tower a second time; clarifying that we instructed to proceed straight while 2 other aircraft were crossing in front of us. The tower did not acknowledge; and the crew proceeded to the FBO without further incident.'