I don't know how, and I'm just curious if you can.

From what I know, you cannot generate pets with points. You have to find a pet essence and use that. There are different types of essence, that have different trait point values. If more uncommon an essence is, the more trait point it has. When you are generating your pet, it takes two points to add a visable trait and one for a hidden trait. So, if you want more points so you can add more traits, you have to get a higher level essence that comes with those points, you cannot add point to an essence. Hope this helps!

Hmm. Ok. Thank you!

We have a guide here to Generator Essences you can refer to for a breakdown of all pertinent information.

(Also, Hidden traits cannot be added to a generated pet- the word you want is actually Carried trait. Hidden traits are traits 'hidden' by a more dominant trait on the same slot (Vis trait might be, say, BB, the Carried version would be NB, where N=no vis, and a Hidden would be, say, BH, or BD, with the H or D being the Hidden))