Three Channel Resistance

Typical class D is a one-channel mono amp.....you must be referring to class A/B stereo amps.  And you want to know how the impedance adds up in Tri-Mode, did I read you right?  I answered that in this post recently.

The impedance loads are not added together because of the passive crossover you must build and use for tri-mode operation.  Power is made to the bridged impedance load at it's frequency range, and power is made to the stereo pair at their impedance and freq range.  In your case the two channels will each make power at 4 ohms to each mid driver, and will also make power at 2 ohms each to the bridged sub...  depending on what frequency is being hit at the moment.

The crossover might consist of a cap value of 265 uF on each of the (+) mids, and a coil value of 4 mH on the (+) bridged sub for a 150 Hz 1st order crossover.  Here is a calculator.  Check into this more as I may be off on the values.  And the amp's LPF and HPF are not used;  you set it to full pass if in tri-mode.

You would just call it "tri-mode" operation at the individual impedance loads you have attached to it (4 ohm stereo + 4 ohm bridged).   The amp will necessarily work harder and get hotter using it this way but not because the impedance load is low....it's because its working double-time.  And if you don't have the proper crossover in place and fully functional, the amp will indeed see lower impedances.  That is not something you want to try.