Since you didn't post the Make & Model of your HD78XX it may be difficult to answer your question.
I would download GPU-Z and run it and see which HD78xx you actually have installed.
But guessing I used a Sapphire HD 7850 GPU card and the maximum supported Monitors is "3".
While a XFX HD7870 supports 4 Monitors.
Also the Sapphire HD7870 Flex supports 6 Monitors.
So depending on which HD78xx you have and the manufacturer will depend how many monitors it will support from 3 to 6 Monitors.
Edit: On some of the older GPU cards, You can only plug in one Monitor to two same ports. Sometimes 2 Ports (HDMI or DVI) may share the same chip so if you plug in one monitor on one HDMI port the other HDMI port will be disabled.