Is it possible to strenghten a ferrite magnet by forcing a field just a little greater field over it?

I have a sub-woofer magnet that’s too weak for what I need.

Probably because of it design, it came from a very cheap speaker and it has a way too wide air gap. Here’s a cut away view of a model of it I reverse-engineered:

The flux density at the middle of the gap only gets to 0.75 T, which is a little small for what I need.

There are two possible interventions I could do. The most effective but possibly not so easy is reducing the gap with a new top plate. The other would be somehow strengthening the magnet. And I could do both to get better results.

I found out, through several simulations of a reverse-engineered model of it on FEMM, that using the DC power supplies I have and placing a static coil inside it, the best I can do is increasing the field density (B) inside the magnet by 12% while the coil is on.

My question is: Could I get to strengthen it by doing this? Like letting it with this coil submerged in water (for cooling) for a day or so? Could this have any effect?

Or would I need a much much stronger field for this to have any permanent effect whatsoever?