Simultaneous Meetings in 1 Account

My company is on the Business Plan. Staff are all Basic Members of this plan. 

We provide networking opportunities to our clients. As part of this we set up meetings between individual clients and network matches. We can have up to 20 of these meetings happening simultaneously on any given day. What we would like to be able to do is set up the meetings all through one or two Zoom accounts for the client and their match to meet using the link we provide. This, as you might imagine, has not been working quite as planned. It's important that we are the ones who control the meeting link so that we can adjust things if anything happens either with the client, the match, or with us. We have other meetings that happen simultaneously out of one account, but we believe we've been able to get away with it due to having alternate hosts that are from within the same organizations. So this leads me to ask: 

Is there a Zoom Plan that would allow multiple simultaneous meetings in one account without alternative hosts?

Is there a Zoom Plan that would allow alternative hosts from outside of the organization? 

There are many reasons as to why we don't want to do breakout rooms, but if there's another solution that might solve this for us on Zoom (even if it means upgrading to a different plan) I'd love to hear thoughts! 

Thank you!