PWM transistor connection

I have the following configuration:


Three PWMs come to the first three NPN transistor bases to regulate the light intensity of each colour of the two common anode RGB LEDs.
The last NPN transistor, the one circled in red, should control the TOTAL light intensity of the RGB LEDs, but of course I don't think this kind of emitter follower configuration is correct.
How should I connect the RGB LED anodes to the last transistor to make the circuit work properly? Should I instead use a PNP transistor?
Note that Vcc is 15 V because I'm going to add more than two RGB LEDs, maybe six or seven, so I will need more power.
The resistors on each LED cathode are present, I only forgot to draw them on this circuit I'm sorry (also the resistors on RGB LED anodes are unnecessary).

p.s. At least I managed to solve this issue via software (adding an internal PWM which monitores total light intensity), but I really like to know what would I have to do to make the circuit above work properly!

See attached file. In PWM if duty cycle is more then ON time of pulse is more i.e., high state of pulse is more. More the duration of ON time more the brightness of LEDs. If PNP transistor is used for Comman Anode connection then base needs 0 to turn ON the transistor. If duty cycle is more then OFF time of pulse will be less. So, transistor turns ON only for a small time. LED brightness will be less. PWM operation is inverted. If you use NPN then more the PWM duty cycle more the duration the transistor will be ON. LED brightness is more.

If NPN transistor is OFF then Vce = Vcc. If NPN transistor is ON then o/p (Vce) = 0V.
See what happens for PNP.


https://dduino.blogspot.in/2012/03/arduino-uln2803.html