Hi,
Instead of searching for the microcontroller with 6 external interrupts use this common method.
Connect the 6 interrupt lines to the 6 input pins.
OR the interrupt lines and connect the output of the OR gate to the single external interrupt pin.
Whenever any of the interrupt lines become high the OR gate will produce an output which interrupts the microcontroller through the single external interrupt.
Now inside the ISR you can check which line has become high by simply reading the input pins one by one.