I'm Homebrewing a psionic Artificer subclass, and several features have damage increases at higher levels. I'm wondering if I can add a damage increase at 13th level, which has no features on the Artificer Table. As far as I know, no Artificer subclass has damage increases, so I can't really look to examples. There is, however, two more spells added in the subclasses spells in every subclass. So can I increase damage at 13th level, or should I stick to 3rd, 5th, 9th, and 15th?

That depends. What exactly do you mean by “damage increase?” 

Increasing the damage die from 1D8 to 1D10.

I get that, but the damage die for what? For an Action or for something else?

These are the specific abilities:

Psionic Defences
When you reach level 5 in this class, you are able to enhance the defence of your infusions with your psionic abilities. When a creature you can see wearing (armor) or wielding (shield) an item you infused being hit by an attack, you may take your reaction to rebuke the attacker. They take 1d6+INT psycic damage. This damage is improved at 9th level (1d8+INT) and 15th (1D12+INT).

Your Worst Nightmare
At ninth level, your weapons are empowered by showing people their worst nightmares. As a bonus action, chose a creature that has been hit by a weapon affected by your Psionic Blade ability this turn. That creature makes a WIS save. The creature takes 1D18+INT psycic damage on a fail, and half as much on a succses. This damage increases at 15th level (1D12+INT).

And you want to know if you can put the bump to 1d12 at 13th level. Technically yes, you can. However it would feel weird.

Ok, thank you for the answer!