The Hardware you have will support up to six displays, provided no more than two are "legacy" displays. "Legacy" display is anything other than DisplayPort or Mini DisplayPort. To support more than the first two "legacy" displays, you need to use ACTIVE adapters, available for under US$40.
The built-in HDMI port counts as a "legacy" display.
The second could be supported with "any old HDMI adapter" from a Mini DisplayPort (plugs into ThunderBolt port, and picks up a subset of ThunderBolt equivalent to Mini DisplayPort).
The third, and fourth, and further would need ACTIVE adapters to HDMI. lllaass suggested one made by StarTech above.