I was thinking that the concept of Waving Hands game could be adapted to the Decktet.
Gestures become Suits (let's call them Runes, for example). Instead of placing one gesture per hand, players would lay down cards in sequence horizontally and each suit in a card would be a "gesture" from a hand. This way, two lines of suits are made, and the each form one sequence for spells.
As you're more limited in what suits you can use (in Waving Hands you can freely choose each gesture), spells would have to be shorter too. Example of spells could be Wyvern, Sun, Sun for a Fireball spell, or Wyvern, Wave, Wave for an Ice bolt. I've made a small table with some spells, using the meaning of each suit as a guideline for combining them in to each spell.
Another idea I had is that the players play the cards on the table making a 2-d grid of cards as they play. When a player places a card so that when a sequence is completed (maybe restricting spells to horizontal from left to right and vertical from top to bottom) the spell is released. This way players have to take advantage of the growing board and can hinder each other efforts.
Of course, this would dramatically change the game…