We did play with these possibilities but this version of the game was by far the best.
There is a exactly one card for each possible combination of symbols up to rotation. This has the effect that for every standard "corner" there will be exactly three cards that could fit there. This mathematical approach is the same as the original dominoes which has exactly one tile for each possible pairs of numbers (as the only rotation is by 180 degrees).
Thus more cards is directly linked to more symbols. Unfortunately the number of cards grows very quickly. It is 24 cards for 3 symbols (our game), 70 cards for 4 symbols, 135 for 5 symbols, 246 cards for 6 symbols ...
There is a potential to consider an expanded version using 4 symbols (70 cards) but since we wanted to keep the kickstarter focused we have settled for now on just the 3 symbol (24 card) version which we feel is the best version.