Air Carrier pilot departing PSP reported ATC amended their initially assigned altitude to avoid VFR traffic overflight not in communication with ATC. The reporter stated this occurrence has happened in the past and recommends changes to airspace rules; procedures; and published advisories to avoid conflictions with VFR GA aircraft.

Narrative

Climbing through around 3;500 feet SoCal Departure cleared us to climb to 15;000 feet on the Cathedral 1 SID. We were then advised of traffic crossing above us. We were looking but did not see the traffic. Subsequently ATC cleared us to level at 6;000 feet for traffic; shortly thereafter we received a level off RA. As I responded to RA and aircraft was beginning to level at around 5;700 feet we were immediately 'clear of conflict.' The entire event happened quickly and was resolved in what seemed like a couple seconds. As far as we know all separation was maintained and the 6;000 clearance altitude would have been sufficient. The Controller was not in radio contact with our traffic. Clear of traffic we were again cleared to 15;000 feet and to a down line fix.It seems that traffic in the PSP continues to increase and the lack of required communication in the PSP area and TRSA creates these issues. My last 2 visits to PSP in particular have involved extremely busy airspace and controllers. I believe VFR charts and procedures for operating in a TRSA may not be clear to many GA pilots and may not be sufficient for separation in the near future. It may be time to redesign or reclassify the airspace around PSP. As traffic continues to increase; more positive air traffic control will help controllers with volume and separation of aircraft around PSP and could assist VFR traffic transitioning Banning Pass. Also a turbojet specific SID may be less complex than the current SID's and allow crews more time to look for traffic and to see and avoid. It would be beneficial for crews to add a note in our Jepp pages about the high level of traffic operating in the vicinity of PSP and that communication is optional for VFR traffic operating in the TRSA; so many aircraft; even 'close' to the airport; may not be in contact with ATC.