gluons emitting gluons

Electromagnetic waves can be put in a box and quantized and the
result is photons, but gluons seem to be a case of a box within a box
- gluons can emit gluons.Is there any evidence that photons can emit
photons - shouldn't the force carrying particles have more in common -
shouldn't we be able to just look at a particle at random and say that
it has property x, property y and property z, therefore it is a force
carrier?

.

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