one would also have to figure out how to recharge the batteries from PV on a priority:

I don't think that's difficult...

... unless you want to keep changing your mind.

Most inverters have RS485 ports which communicate using Modbus.
There are a number of micro-contollers, such as a Raspberry Pi, to which an RS485 port can be added.

Enter what you want to do into an AI Chatbot, and it will generate the code for you in about 10-secs.

Once the code is downloaded into the micro-controller, it would continue to operate according to those conditions.

However, if you wanted a user-interface which you'd periodically use to change the charging schedules, then that's a lot more work.

I'd suggest you need to cultivate a rapport with a teenager who would really enjoy doing this for you...
... and probably use it as 'evidence' to secure a university pl;ace once they leave school.

Here on the Forum we have enough technical knowledge to help with configuring those two battery systems to supply power within the home.
They obviously mustn't fight each other, nor spend the night taking stored energy from one battery and transferring it to the other!

And one would also have to figure out how to recharge the batteries from PV on a priority: battery 1, then battery 2, then export. I assume that would be tricky.

This is both from an energy management perspective, where the operation of the inverter can be optimised to meet any specific contractual commitments, as well as for basic control. Like one of the RJ45 ports enables remote restart. 

They are migrating away from the low-voltage systems through which they made their name, and investing in high voltage All-in-One units for the future.

The technology is different, and based on a new generation of embedded inverter which supports 3rd-party control if required.

There's nothing wrong with that, and it is likely to create market opportunities for GivEnergy AIO products to be installed in social housing for example.
But the change of directions means that the existing user-base can't take advantage of the new style batteries.

Yes, they still have the earlier design of battery and separate inverters in their product line-up.
The Gen 3 9.5kWh was released in Nov'24, but GivEnergy are unlikely to state for how long their earlier models will continue to be manufactured.

Remember that the GivEnergy option would most likely be a High Voltage battery (above 75v), and therefore all future changes and maintenance can only be done by a qualified electrician.

I agree, with two systems, the working modes need to be carefully assessed, as they may just interfere with each other. Both may need to know the tariffs, etc 

However in terms of voltage, this GivEnergy "Gen 3 9.5kWh" battery, albeit expensive at over £200/kwh, is low voltage.

If both were configured to allow Zero Export, then the question becomes easier to answer.
That's because the DNO would most likely approve your G99FT Application immediately.

Here on the Forum we have enough technical knowledge to help with configuring those two battery systems to supply power within the home.
They obviously mustn't fight each other, nor spend the night taking stored energy from one battery and transferring it to the other!

Remember that the GivEnergy option would most likely be a High Voltage battery (above 75v), and therefore all future changes and maintenance can only be done by a qualified electrician.

Is there any technical reason, why, for example, I couldn't have an Eleven system and a Givenergy system connected to our house?

The best price point is likely to be with 48-52V batteries of 16khw or higher capacity. 

The risk of fire when fitting them at home with a matching inverter, etc is low. Personally I am not using such a matching battery. But since Fogstar stated that it is not a problem, I still assess my risk as low. 

I would not see the app for the inverter as very critical, even less so for a battery. While anyone with a HeatPump would want to keep an eye for set temperature, costs, etc, I think that is unlikely with an inverter..

Lithium Titanate (LTO) has a base cell voltage of 2.3v, meaning that 22 cells are required for a nominal 50v battery.

LTO technology has a number of attractive features, including

• can be charged/discharged below 0°C
• longer lifetime than LiFePO₄ chemistry (more cycles)