SR-71 Blackbird has the right solution. Your mobo's only SYS_FAN header does appear to use proper PWM Mode to control 4-pin fans, so a 4-pin fan Hub such as Blackbird suggests is the right way to control many fans from one header.
HOWEVER, that Hub will only work if all your case ventilation fans are of the newer 4-pin type. The problem is that many cases now come with 3-pin fans, and plugging those into any 4-pin fan header results in the fan's running full speed all the time., with no control. 3-pin fans require what is called Voltage Control Mode. The website for the case you specified says it comes with five 120 mm fans pre-installed, but does not specify which models, so I can't tell from here which type they are. The site does say the case includes its own "fan controller", but what that means apparently is that you can manually set your fans to High speed, Low speed, or Off. This is nothing like automatic control by a mobo header. This info also suggests that you MAY have to do some fiddling around with the wires for the pre-installed fans so that they can be plugged into a standard fan header.
IF your case fans are really of the 3-pin variety, there is one Fan Hub on the market that CAN control 3-pin fans while using a mobo 4-pin PWM Mode header for its control signal source. It is the Phanteks PWM Hub. Apparently is uses the PWM signal to create its own group of six 3-pin fan headers operating in Voltage Control Mode, so it can power and control any mix of 3- and 4-pin fans. That might be what you really need.