External Thunderbolt drive and Monitor from same port

I have recently run into a similar situation as yours. Both of the proposed solutions below do not use expensive gear like thunderbolt docks or monitors, and can achieve the same (or similar) desired end result.

1. This Thunderbolt-to-Dual-HDMI adapter allows your to connect two 1080p monitors to a single Thunderbolt port, and have both those monitors act independently from one another (ie. they are not mirrored). The adapter is also passive, which is nice.
2. Buy a Chromecast. This solution is sub-optimal, and is dependent on you having a decent internet connection, but with this $35 device, you can stream a browser tab, your desktop, audio, video, and more to an external monitor. The third monitor can then be added with a simple Thunderbolt-to-HDMI adapter.

This is a really interesting question that gets to the heart of how display signals travel over Thunderbolt.

Your mac is capable of driving two "Thunderbolt displays". The special thing about the thunderbolt display is that it is capable of "pulling" the display signal out of the thunderbolt signal. This specifically is called "demuxing" (de-multiplexing). So technically, thunderbolt is capable of carrying two multiplexed display signals.

In contrast, when you use a displayport adapter on a thunderbolt chain, the bus driving that port from your mac is only capable of sending that one display signal since it is not being multiplexed on the wire.

The Elgato dock (or OWC dock) is capable of doing the same thing as a thunderbolt display, in that it is demuxing a display signal from the thunderbolt wire to provide an HDMI port. If you are using the HDMI port, you can't plug a displayport display into the other end of the thunderbolt chain -- there is no component to demux the other display signal. You COULD use a thunderbolt display in this position.

But, you have one other option! If you buy a SECOND Elgato device and add it to the thunderbolt chain, you now have a component to demux a second display signal to another HDMI port. Then you can use the two HDMI ports to drive whatever displays you want!