I've posted the "how it could be possible" but not whether I'd like it LOL
In short: No. Even conceptually, I think anyone who does is essentially confusing types with egg-groups without realizing it.
I do see that there are pokemon who show aspects in their design that sometimes aren't covered with 2 types.
But you also have to understand that looks and types are not necessarily related. Or at least not in the sense that many assume.
The prime example would be the common mistake of people thinking "looks like fish"="must be Water type". It's just not true. One is a description of what kind of creature it is, while the other is about what element it excels well.
And that goes for all types.
The issue arises mostly with the "species" types (Bug, Dragon, Ghost..), and the poorest type concept: Flying.
(probably 99% cases that currently look like they require triple types is because of at least one of these types)
The thing is, people don't treat those as types.
One should think about them as elements even though its not straightforward. You don't have to be an insect etc to have powers associated with the Bug type, it is just that quite many happen to be those two at the same time, so to say.
Since Pokemon aren't limited by their types on what moves they can learn (which is a whole different subject), the number of possible types comes down to this:
How many types should Pokemon have STAB on?
How much complexity should be in weakness/resistances when more than one set (type) are in play?
To the first question, I'd actually answer that all pokemon should have the same amount of STAB (which would require either all pure types to be given a secondary Normal type, or rework the STAB mechanic so Arcanines Fire STAB is stronger than say Infernapes Fire STAB due to also having a Fighting one)
The second, its crystal-clear: 2.
However even here, and without bringing triple types into discussion, in my opinion it's already being handled poorly. weaknesses should NOT straightforward mutliply (resulting in a huge jump to 4x, which is severely crippling to the point where a pokemon is crap just because it combines types that share too many common weaknesses).
Anyhow,
so in the end, when you look at one of these examples, like say the famous Charizard, its types are Fire and Flying. It is not Dragon TYPE, but it is a "Dragon" in egg-group terms. Egg-groups are the thing that matters when it comes to "kind".
Or (to also address the "Flying" confusion) lets say Flygon. Its types are Ground and Dragon. People would assume Flying due to it having wings that enable it to fly. Well guess what, seems like merely having wings and flying with them, doesn't make you an expert in flying techniques.
At the same time, there could be a Pokemon that shows no sign of being airborne, but BE a Flying type.
There is only one issue with this: Ground immunity.
Gamefreak really needs to address this one, not just for the sake of Flying type pokemon, but for all the bugs and whatnot who are capable of flight or have other reason, which sometimes result in a poorly excused "Levitate-fix".
All they have to do is make Flying resist Ground attacks, and then make "airborne" a mechanic determined for each pokemon separately. Heck it could have several levels:
-Level 0: fully on ground
gets hit by ground-based moves as expected
-Level 1: has ability to be airborne, but not all the time (small birds, bugs)
there is a 50% chance ground-based moves will miss due to it being airborne at the time
-Level 2: fully airborne for unlimited time (or until fainting), and the preferred stance in battles
All ground-based moves are a miss 100% of the time.
Why did I write ground-based instead of Ground type? Because those should be separate things too IMO. Something like Mud Bomb should be able to avoid this immunity, while something like Rollout would be also considered gorund-based and therefore avoidable by the explained mechanic.