They can squeeze more out of him but its a cost to benefit ratio thing.
Players want increases because they have a history of long service and 'hey I have done this'. Its a classic trap in American sports where a team has a superstar that has been there for years and has performed. They then get re-signed and have an expectation of a contract based on that history of performance. If they don't get that, its disrespectful and 'how can they insult me, and the fans by not paying me what I am worth and given to this team'. The GM then gives them a stupid offer based on that history and not what they are going to produce in the future over the life of that next contract. The superstar then ages and does not perform at the level they use to or commensurate to their pay and the team is left with a former superstar that has aged and not producing with a massive contract and hamstrung the teams salary cap.
If you do the exercise...
Can you get more seasons out of Sigmund at 33-34? Yes.
How many? 1 maybe 2. 3 at a massive stretch
Will they be improved years? Unsure although history on him says yes but history in general says unlikely.
Best option: 1 year at the same he is on now. You then evaluate the following year and whether the team still want him based on his performance and whether he still wants to play for the amount offered, you offer him a new deal based on that.
The club has a history of being smart with situations like this and Leo is the one that comes to mind coming off Terry money and being offered a deal more in line with his use/role in the team. I do think if Ben and the club are smart/realistic, he is a 1 year deal guy now. To offer him a 2 year deal would be crazy.
"Phoenix till they lose"