Opening SASU in addition to Auto-Entrepreneur in France

To recap on my situation: I have an auto-entrepreneur business in the services category (teaching yoga). I teach from an apartment which I bought (not as a droit au bail but as an ordinary apartment which I have converted into a fitness studio). I sublet to other auto-entrepreneurs (Pilates, fitness etc) who pay me an hourly fee to rent the space. Currently, I pay tax on their rental income as ordinary rental income and not as income to my auto-entrepreneur business.

By end 2018, I project my auto-entrepreneur business will turnover around 32K. The subtenants currently contribute around €500-€1000/month in rental. My goal is to work less in my own business and have more income coming in from the studio sub-tenants/freelancers and their teaching (I aim for €2500/month in 2019).

The problem is, in order to do this my business would provide the majority of the clients to these freelancers, they would use my booking system and website and would work under my auto-entrepreneur ‘brand’.

Would it work for me to keep my auto-entrepreneur open for my teaching/work and open a second business (you mentioned a SASU once upon a time) for the ‘rental’ side of things?

Really aware not to get my wires crossed and want to do it right.

Thanks for your advice,