This MacRumors article notes:
Apple's notes one other caveat about the Thunderbolt display: older
Mini DisplayPort displays won't light up if they're hooked directly
into the Thunderbolt port on the newer LCD. Macworld's testing found
that Mini DisplayPort LCDs can be added to a Thunderbolt chain and
work as normal by hooking them into another Thunderbolt peripheral.
It's unclear why simply hooking the older monitors directly into the
newer ones doesn't work. For best performance Apple recommends hooking
the Thunderbolt display directly into the Mac's port, then hooking
Thunderbolt storage devices into the display's relevant port.
From Apple Support's KB:
Mini DisplayPort displays will not light up if connected to the
Thunderbolt port of an Apple Thunderbolt Display (27-inch). Displays
connected via Mini DisplayPort video adapter to the Thunderbolt port
of an Apple Thunderbolt Display (27-inch) will not work. Connect Mini
DisplayPort displays directly to a Thunderbolt port on a
Thunderbolt-capable Mac or to a compatible Thunderbolt peripheral.
If the Mini DisplayPort display is connected to a Thunderbolt peripheral, the display should be connected at the end of the
From another Apple Support KB:
Connect Mini DisplayPort displays directly to a Thunderbolt port on a
Mac or to a compatible Thunderbolt peripheral; do not connect a Mini
DisplayPort display to a Thunderbolt display. Use only one Mini
DisplayPort device in a Thunderbolt chain. You cannot use a Mini
DisplayPort to Mini DisplayPort cable to connect an iMac (Mid 2011) in
Target Display Mode to a Thunderbolt chain. See iMac (Mid 2011):
Target Display Mode does not work with Mini DisplayPort cable for more
I don't have the right hardware to test this setup, but the article/KBs above imply that driving multiple monitors may be possible, depending on your MBP model (see this KB for more details) regarding the number of monitors that are supported. Some MBPs with integrated graphics can only support one Thunderbolt monitor, which may preclude three monitors from being used together.