You need to get with your solar professional/electrician, as you are getting into interesting territory.
One of the advantages of the home integration system (HIS) is that you can continue to use solar during a power outage (you can't without batteries otherwise), and you can also add LG Chem batteries to it to have back-up besides the truck. This requires what Delta(inverter manufacturer) calls a Microgrid Integration Device, which essentially disconnects your house from the grid in a power outage.
You can get an inverter with the HIS up to 10 kW (which is what I have), it doesn't cost anymore, but you can start running into code/compatibility issues with the sizing on your main, you aren't allowed to have potential to feed it with more than 120% of bus rating. (so if you have a 200A service, you have the 200A main breaker (or you would on a new install), and then you would be limited to adding a 40A breaker to back-feed solar, which limits you to 7680W. They now make solar ready mains, with a 225A rated bus, that allow you to go up a bit from here, but unless you have a 400A service you are nearing the limit.
I think you could add the 4kW BDI (bi-directional inverter that comes with the HIS), which still requires a 50A breaker but can only feed 4 kW solar (will feed full 9.6 kW in outage), to possibly get around this, depending on your local AHJ. In either case, there will be some legwork involved with making sure the two inverters are able to play nice, you might need to make sure your existing inverter is tied in before your MID device so it doesn't back-feed in an emergency power situation.
There isn't a lot of technical support available for this system.