There are ways to make all varieties of double team characters work.
"Standby and Tag out" Types, where the two characters serve effectively as a stance character with some variety in how they are tagged out. If they tag in and out into the same place it really is like a stance character 1:1, but if one is in standby and the tag out starts controling them from their own position, you get something like Hisui/Kohaku with back and forth juggle combos. This kind is the simplest to balance since it is in most ways the same as a tried and true stance change character; just make sure neither one of the characters cover matchups perfectly over the other.
"Carl" Types, for lack of a better word, where the primary character has their own moveset, and the other character acts as an extension of the first's moveset by standing by, teleporting in for various assist moves, or otherwise being given orders by the primary character. AquaPazza is full of Carl Type assists. This kind is also quite easy to balance since the design by itself lends to complex set ups and an intensely strong neutral game. Just ensure that the reward for their strong neutral game is on the lower side and they'll have to make use of their better traits just as every other character does to compensate, with the added benefit being that those better traits are some of the most important ones in the game.
Constantly Active or "Ice Climber" Types- where both characters are always out with an active hitbox and can be tossed around and comboed individually with impunity. This kind of character is difficult to balance, but very possible; it is just difficult to balance because it is the newest variety of double team character base out there so nothing has been tried and proven. I feel that the important thing about making this kind of character is to ensure that if the characters are designed such that they can be seperated, or that one can be killed before the other, that the single character still needs traits and a workable moveset to put in work necessary to do small setups and short rewards. They have to work harder and use their neutral game to the best, knowing that they can not get super powerful rewards. So they have to be competent on their own, with a weak reward game- Very Low Risk, Very Low Reward, if you want to think of it that way. On the other hand, when the character is twofold, they have to be carefully made such that they do not get too strong of a reward either, or the strong neutral game the character has has no drawback. So this character base comes down to three aspects- Keep them from being too good with both characters present, keep them from being too horrible with only one character, and keep both states of the character differentiated in favour of wanting to keep both of them. You can see why this is difficult to balance, because these aspects are almost contradictory. Well that is why it helps to look at this character in the Risk vs Reward sense. With one character, they are a low risk, low reward character that has to work hard to get multiple smaller hits over a long period of time; They get easy hits in but they aren't super threatening by themself, and one small mistake can mean the opponent gets the opening to do a more rewarding combo on them. With two characters, they are still effectively the same low risk, so the simple question is, how good should their reward be with two characters? You make them low risk high reward and they can roflstomp most of the cast and get beaten by the other small portion- they become a polarising design, not very fun at all for either party. Myself? I think the best reward is still a little on the lower side, and only marginally better than with one character. The reason being that with two, the task of getting single hits becomes much easier, and setups become a simple affair, so they become a very low risk character, knowing that they have more lenience than other characters are allowed. So the goals are then, hopefully, met well- With two characters they are a high-tier character, and with one, they are still a solid Mid-Tier that is far from helpless. All the second character does is make it a little bit easier for the player, a little brace to fall back on, so to say.
I can't think of any other double team varieties myself, but anyone else is welcome to comment on the archtype.