It's possible to cross breed any gene - but do you want to? What is your goal? Will it support your goal?
Example: pure cherry red x pure irid
Both are dominant colors, at least partially. You will probably end up with irid body with red fins, irid body with red wash on fins, few to no solid irid. As for red results; cherry red with irid (dots) on body and or irid lines on fins. Probably no solid reds.
Your female looks like a classic cherry red (not sure - picture not clear). Try reading
Color Genetics Guide
for starters. Read as much as you can find on color genetics. Then determine the direction you want to go.