If you have access to StreetSmart look at the all-in-one trade ticket. Haven't done more than 4 sides in a decade, but it should have been 16 by now. They'll need to be identifiable strategies and not just random legs alone.
Thank you for your suggestion. I found this:
https://help.streetsmart.schwab.com/SSCentral/1.0/Content/Placing Option Orders Multi Leg.htm
Which states "up to four legs".
I will reach out to them to confirm.