daisy chain DisplayPort monitor

I understand that one cannot daisy chain my dell U2715H monitor with my Thunderbolt Display using a DisplayPort cable plugged into the thunderbolt port on the back of the thunderbolt Display. I've tried and it doesn't work. I've also tried inserting another thunderbolt device in between the Apple display and the dell monitor and this also does not work well, the monitor turns off and on frequently.

So my question is, are there *any* monitors out there other than a second Thunderbolt Display that will work in this configuration?

Maybe a monitor that uses actual thunderbolt rather than DisplayPort? Do those even exist?

My MacBook Pro has a second thunderbolt port which I've run the dell from difextly, but I would like to reserve one of the ports strictly for audio interfaces (this is being used in a recording studio) and the second for displays and other peripherials.

Thanks!

Geoff