Hello,
I think the starting point is with a form of means testing, for anyone looking for a pension increase.
As an interim measure, let's help the elderly who need help, but not those who don't.
To keep things simple, in the shorter term, the elderly could make an annual self declaration as to their income and personal assets (excl. their personal residence). Anyone up to certain, specified, limits, gets the additional payment, but the others don't.
That could be an interim solution for say the next 10-years, while better longer term arrangements are put in place.
Ultimately, the plan would be to freeze all state pensions, with people getting plenty of lead in time, to start making their own arrangements.