The maximum number of 10 AWG conductors you can add to the box is 4 with some space left over.
Each 12 AWG wire has a volume of 2.25 cubic inches, so the six wires take up a total of 6 * 2.25 = 13.5 cubic inches.
This leaves 27 - 13.5 = 13.5 cubic inches of space for additional wires.
Each 10 AWG wire has a volume of 2.5 cubic inches, so you can add 13.5 / 2.5 = 5.4 additional wires to the box.
However, according to the National Electrical Code (NEC), you can only fill an electrical box to 80% of its capacity.
This means you can add a maximum of 0.8 * 13.5 = 10.8 cubic inches of additional wires to the box.
Therefore, the maximum number of 10 AWG conductors you can add to the box is 10.8 / 2.5 = 4 with some space left over.