When you cast the summon monster spell you then roll a d6 and pick from the list of traits. Can you pick the same trait twice? That is could I have two stats at +2 or have it do 2d8 damage?
You can double up all manner of choices, but only some of them will benefit you:
It has +2 instead of +1 to one stat
As it's setting something explicitly, you have to pick different stats to benefit from stacking this.
It’s not reckless
Yeah, that only works once.
It does 1d8 damage
As opposed to your damage die. This would be a downgrade for a multiclass fighter, for example. Only works once.
Its bond to your plane is strong: +2 HP for each level you have
That's an incrementor, so you can stack it. That might seem a little strong, but having hit points just means you're not dead yet; it doesn't say anything about how effective you are.
It has some useful adaptation
There's more than one possible useful adaptation, so this can stack.
You have to be able to pick the same trait twice, since you pick 1d6 traits and there are only five.
You can't gain 2d8 damage by picking 1d8 damage twice, because the trait only says "It does 1d8 damage", not "does 1d8 additional damage". The 1d8 damage trait just means that it does 1d8 damage instead of its default, which is your damage dice (d4, by default, for a wizard).
You can have +2 to multiple stats, though not +4 to one stat, since it says "It has +2 instead of +1 to one stat".
You can for some, but not all of them. The words are "The monster also gets your choice of 1d6 of these traits", there is nothing about limits, and like mentioned by Quadratic Wizard, there are 5 options, but you could get 6 choices on a perfect roll, so you have to be able to pick some of them more than once.
It has +2 instead of +1 to one stat:
Can be chosen more than once, but only to make more than one stat +2. Because it sets it to +2, rather than adding 1, it can't stack.
It’s not reckless:
This is a bit subjective, but I don't think it should be able to be chosen more than once. This stops it from being reckless (whatever he GM determines that to mean), it doesn't reduce it, so taking it more than once shouldn't do anything extra.
It does 1d8 damage:
Can't be taken more than once, like above, it sets the damage to 1d8, so taking it again doesn't do anything.
Its bond to your plane is strong: +2 HP for each level you have:
Yes, you can take this one more than once because it's an addition to it's current health, rather than setting it's health to a specific number.
It has some useful adaptation:
Again, this is going to be up to the GM. I would say yes. The GM is suppose to give you a monster based on the traits you chose, so if you chose this one a few times, it just means that they need to give you a monster with lots of abilities (it can fly, breath fire, carry a passenger so it's a Dragon.... or something)
You can always talk with the GM about it and maybe get some house rules so you can choose some more than once. The damage one could be re-written to "Increase the monsters damage dice by one stage" or "It does 1d8 damage, +1 for each extra time this trait is chosen". The Stat one could be re-written to "Increase one stat by +1" or something, so you could stack it.
I also like building on this spell for my players, adding options like:
- It has +1 Armor
- Its attacks have 2 Piercing
- Its attacks are Messy and Forceful
- You get to choose from a few options of your summoned monster
- You have a form of telepathic link with the monster, allowing you to tune into its senses (sight, sound, touch, smell, taste, echolocation etc.)
If the GM does not want to allow stacking traits for some reason, they might want to chose to provide more options.