Driving 16-segment displays with MAX7219
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. "That's not a schematic. This is a schematic."

Why it would work

If the schematic of Figure 1 is what you intend then (without reading the whole datasheet) you might be in with a chance. Page 5 says about pins DIG 0–DIG 7:


  Eight-Digit Drive Lines that sink current from the display common cathode. The MAX7219 pulls
  the digit outputs to V+ when turned off. The MAX7221’s digit drivers are high-impedance when
  turned off.


So the 7219 digit pins can't be connected in parallel (unless you add a diode into each line) but the 7221 can as the pin goes high impedance when not driving a digit.

You would need to run the chip in "No Decode Mode" to allow individual segment addressing. See page 8.

Why it wouldn't work

Looking at the schematic it is now clear that when SEG A is driven high that both 'A' and 'K' will illuminate if either DIGIT 1 or DIGIT 2 is low. (Schematic beats wiring diagram.)

Since you have only one common cathode you are beaten.