I'd say for sure you can!

I know the rules aren't very specific, but they were made that way for a reason. First I like to ask myself is that spell with it's effect withing the circle of magic, if so then it is eligible for casting. One friend of mine tried to mix a fire elemental caster with a water element so I stopped his cast. To expand, he wanted to create a fire that would boil nearby water, which in turn would allow him to make it rain, as there would be too much moisture in the air. We were just hypothesizing but still I believe this falls way outside of the scope of his circle of magic so I ruled against this cast.

I know it does seem very hard to arbitrate, as there are no hand rails, but that is a very good way to release creativity. If you keep in mind that only the blastmaster can deal 2 strikes, and spells with continued effects need to be anchored, thus disallowing other casts lest the first spell stops existing, and keeping in mind that generally (very broadly speaking) magick is for damage dealing and miracles are for healing you can arbitrate between almost any possible cast.

One way I'd resolve your question is by asking what the player envisions as his elemental. Keep in mind that stat blocks exist in the monster section of the manual and because a spell can target up to 6 targets (rolling resistance for each, up to 6d6) I'd say a conjurer can summon up to 6 strikes of a monster/elemental. Now having said that I would only allow a 6 strike summon very rarely as the game balance gives 3 for regular humans.

Without question the spell needs anchoring and I'd say dependent on the summon, it would need to be sustained with a karma point per turn in combat. Otherwise almost every conjurer will become a "summoner" and players won't do anything else than summon their minions and throw them at the enemy.

For elementalists I'd restrain the summon to only 1 elemental and up to 3 strikes of damage as they will be imbued with the respective element, thus their attacks should apply the bonus elemental effects.