Ermm... random thought.

[eaglgenes101]

I have thought of elements to be groupable in 4 types (In addition to the 3 types material, cardinal, spiritual):
Free:
Active:
Grounded:
Passive:
 
What do I do with this grouping?

[Pineapple]

Well, it helps that you have some kind of theme separating each group as distinct.

Now, you can choose to rely solely on theme, for example an Air creature "This gains +5/+0 when this is targeted by the opponent. 50% chance to evade targeting." or a Light creature "This gains a 25% chance to deal +50% damage and ignore shields for every permanent your opponent destroys." In this case, the groupings will become thematic guidelines rather than a mechanical series.

Alternatively, you could focus on the groups as a whole. Permanents like "Freedom's Wing-- Shield: For every enemy attack, your creatures gain a 1% chance to ignore shields." The problem with this is that you might be making a card too situational.

[MaTianLong]

I have thought of elements to be groupable in 4 types (In addition to the 3 types material, cardinal, spiritual):
Free:
Active:
Grounded:
Passive:
 
What do I do with this grouping?

You can start to explain what every group does...

[artimies7]

I have thought of elements to be groupable in 4 types (In addition to the 3 types material, cardinal, spiritual):
Free:
Active:
Grounded:
Passive:
 
What do I do with this grouping?

You can start to explain what every group does...

Can that be up for interpretation? I think that would open it up for a bit more inspiration.

[OldTrees]

I have thought of elements to be groupable in 4 types (In addition to the 3 types material, cardinal, spiritual):
Free:
Active:
Grounded:
Passive:
 
What do I do with this grouping?

You can start to explain what every group does...

Can that be up for interpretation? I think that would open it up for a bit more inspiration.

If the grouping does not have inherent meaning then it is arbitrary. I do not see why an arbitrary grouping would have meaning.

[EmeraldTiger]

I say there are many possible groupings that hold thematic resonance.

[ZephyrPhantom]

I personally think it's a good idea to try to develop combinations that don't have much background.

As pineapple said you could go the route of making everything thematically unique or design as if your are considering that specific element combination. I would suggest the former if you're planning to avoid 'cornering' yourself into a forced trio, IMHO. (The shield example in pineapple's post, for example, could easily say airborne/immaterial and be just as fitting.)

[eaglgenes101]

One advantage of this trio combination over others is that it is perpendicular to the quartets.



See?

[OldTrees]

One advantage of this trio combination over others is that it is perpendicular to the quartets.



See?

That is an advantage. However it is shared with 15 others.
Ex:
 
 
 
Good job justifying a set of 16 options down from the much larger number of options.

[shadow303]

The only real grouping of the elements that I personally can see is the grouping of opposites like:
 
 
 
 

Even though that doesn't really work for the last four:
 
I personally would like to see an opposite for every element, like e.g. an element of regularity as opposite of the chaotic entrophy and so on.

Beside that I think there are a lot of possible logical groupings of elements.

[Pineapple]

Even though that doesn't really work for the last four:
 

Hm? I think that the last two elemental pairs are the most defined. You can't really find thematic and mechanical card opposites in for example Fire vs. Water, but in Entropy vs. Gravity you have Supernova vs. Black Hole and Maxwell vs. <pretty much any Gravity creature>, while in Aether vs. Time you have Twin Universe vs. Rewind and Mindgate vs. Hourglass.

[OldTrees]

@shadow303
  order vs entropy (note: not order vs chaos)
  space vs time