Logically of course the 1-4 pips align closely with US Navy flag ranks - so 1 pip officers exist, as do 2, 3 and 4 for Commodore, Read Admiral, Vice Admiral and Admiral respectively.
Again, there is no rank of Commodore in the U.S. Navy.
The ranks of O-7 through O-11 are Rear Admiral, Lower Half (RDML), Rear Admiral Upper Half (RADM), Vice Admiral (VADM), Admiral (ADM), and Fleet Admiral (FADM). They wear, respectively, one through five stars on their collar and shoulder.
Commodore was supplanted by Rear Admiral, Lower Half. Today, "commodore" is a title only, akin to "comandant", usually held by someone with the rank of Captain.