@Ryan R the two additional terminals must be connected to the controlling voltage nodes. They can be the same as the output nodes. Considering below picture:

V(OUTPUT1,OUTPUT2) = 1 + V(INPUT1,INPUT2) ** 4 +* V(INPUT1,INPUT2)^2 * 2 + V(INPUT1,INPUT2)^3 * 3

See section 5.5.1 of the ngspice manual.