Existing Sapphire: Cancel to get New Offers?

[GS]

Have had standard Chase Sapphire card for years. Yet Chase still sends me offers to get a sapphire card with offers of points. But when I call and say I have one already--can you reward me with some points for being a loyal good paying customer for years they say. NO sorry you must have gotten some incentive way back when you signed up.

Do I need to close and reopen this account to get points offered? Would that even work? Can I sign up for a fancier Sapphire (Preferred etc)  to get those points? Seems like not.

any suggestions here?
thanks

[smart brit]

Try applying for the preferred card although it's possible u will be denied if u are denied call reconsideration and transfer to the preferred