As indicated, only one ignite is active at a time. They do stack, but not in a multiple damage kind of way.

Can you have multiple ignites Poe?

You can inflict an additional Ignite on an Enemy - by default multiple ignites can be applied to an enemy, however only the strongest one actually deals damage. Emberwake allows for two ignites to deal damage simultaneously, or three with two Emberwakes.

Do 2 ignites stack?

Using two Ignites on a single enemy champion will not stack. Instead they will refresh.