You will need five US parts if the flash hider is integral to the barrel, six if it is removable.

Your options for parts to replace:
- Flash hider.
- Bolt carrier (from 556). I assume that the standard 553 and the 553R use the same carrier.
- Pistol grip. The furniture is green on these 553Rs, so matching may be tough or just paint. Can use a 556 pistol grip after modifying where it interfaces with the trigger guard. Or use a hogue.
- Hammer (Shooting Sight)
- Sear (Shooting Sight)
- Trigger (556)
- Mag body
- Mag follower
- Mag floorplate
- Stock. Craptastic US made 556 stock vs. M4 stock adapter.

Of these I would swap the FCG parts and use US magazines, keeping the rest of the rifle Swiss.