You just need to buy as many schraeder tire valves as you need for the amount of bottles you want to carbonate. That would be very convenient for when you are planning a party.
mp
Why would you need multiple shraeder or ball valves?
You use carbonator device (cup including) only during carbonation process. Then you unscrew your PET bottle with carbonated water from carbonator (carbonator cup) and use a normal PET bottle cup for storage.
Looks like you are applying siphon bottle concept to carbonated drinks delivered in PET bottles.
Siphon bottle uses excess pressure to push water out of the bottle. It is not required for carbonation*.
What is required is COLD water. The colder the water the more CO2 is absorbed. When water warms up it releases CO2 – that’s why you get pressure release opening PET bottle and bubbling effect in your glass.
*explanation is oversimplified for illustration purposes