Sometimes, even it is very rare, you may see the soldiers or enlisted officers brandishing all three tabs, Sapper, Airborne and Ranger. In fact, it is possible to get all of them, but as I said it’s not so usual.
First, the Ranger and Sapper tabs are regularly awarded for completion of the respective schools that award them upon training completion. A soldier or operator who meets the minimum requirements can attend Sapper School and Ranger School, and anybody who successfully completes both schools (courses) will have both tabs. The completion guarantees you the right to wear those patches and badges on your shoulder.
The Ranger tab is widely known, but the Sapper tab (introduced in 2004) is awarded to a service member who may or may not hold the military occupation specialty code (MOS) designation as a Combat Engineer (Sapper), but must have graduated from the Sapper Leader Course (SLC), that the U.S. Army Engineer School at Fort Leonard Wood, Missouri, operates.
The Airborne tab looks similar to the above two tabs but is actually part of the unit insignia of the various Airborne units of the US Army. Any soldier assigned to one of the units thus designated will have that tab, whether or not they have completed the Basic Airborne Course and have been awarded a Parachutist Badge.
So any soldier who has earned the Ranger tab and Sapper tab, and is also assigned to an Airborne unit will have all three tabs. Totally possible. Or even have a possibility to wear also Parachutist Badge if he successfully complete the Basic Airborne Course.
Three tabs example
The best example of the soldier who has earned all those tabs is the SSGT Robert Miller from 3rd Special Forces Group (Airborne). His citations show that he has a CIB, parachutist badge, Medal of Honor, ASF and ranger tab.