In the US, the license and ratings are considered a privilege. Therefore if you had "Robinson R-22 and Bell 206" on your EASA license, and you used that as the basis to get an FAA license, you are restricted to flying those aircraft types on the FAA license.
Is subject to the limitations and restrictions on the person's U.S. certificate and foreign pilot license when exercising the privileges of that U.S. pilot certificate in an aircraft of U.S. registry operating within or outside the United States; and
Note it states "and foreign pilot license".
The only way to add other types is to get the EASA rating or complete a full FAA checkride---one that is not based on 61.75