The moves follow calls to re-sign Matt Doorey (2025) and J'maine Hopgood (2025) in recent times, while the likes of Reagan Campbell-Gillard, Ryan Matterson and Junior Paulo have all been locked in long-term over the past 24 months.
The Eels may look to add some parts around them in the coming months given the club's failure to reach the finals in 2023, but for now, they continue to sign internally.
Cartwright's contract will see him remain in the blue and gold until at least the end of the 2025 season, while a three-year extension for Greig means he will stay at Parramatta until at least the end of 2026.
"Bryce has an enormous amount of skill and was one of our most consistent players this season. We look forward to seeing him continue his great form next year," the club's head of football Mark O'Neill said in a statement.
Meanwhile, the Eels took Greig from the North Queensland Cowboys system and he played an increased role at the Eels in 2023, with his fitness being a major improvement.
“It has also been exciting to see Wiremu take his game to another level when he stepped up in the front row in the absence of Junior and Reagan this season and displayed a level of leadership beyond his years. He showed just how hard he is to handle, making a tremendous contribution to the team,” O'Neill said.