How to remove seized mixer bath tap diverter cartridge

[cmarkr]

I've got a mixer bath tap/shower hose. The diverter is seized. Shown in photo is what I believe is the diverter cartridge (bottom) with the internal splines but there is no flats to unscrew it. I believe it therefore needs pulling out (retained with oring?) but it's recessed except for about 5mm. How do I get it out without being able to get anything around it to get any purchase?
The bit on the top screws off but doesn't expose any access behind the diverter cartridge.
I've tried descaling with citric acid but no luck.

Do I need to turn water off before removing? I assume not. There is no accessible local isolator.

 

[oldbuffer]

1. As long as you turn the taps off you don't need an isolator.
2. What is underneath the diverter valve? - sometime a cap which can be unscrewed.
3. Unless you know the make and model of the tap, and it is relatively new, it is almost impossible to find spares. So unless nothing is broke but just seized, taking it apart may not get you any further.

 

[cmarkr]

Thanks for the reply @oldbuffer

Here's a photo of it all assembled. It's the shower hose outlet underneath.

The other bathroom fittings are duravit and hansgruhe so it may be one of those. The bath is tile sided so it would be destructive to replace the whole unit. There's only a few mm between it and the wall behind.