Characters who change from a "normal" form to a super-powered one are a classic theme not just for Superheroes but also in Fantasy and even in Science Fiction. Here are various manners of handling this gimmick in BASH.
Obviously there are Powers that already allow changing form, like Mimic and Shape-Shifting. But those are too varied for what we want here (unless you give them a Limitation on the number of forms taken, of course.)
Note: Remember that Shape-Shifting cannibalizes the character's Brawn or Agility points to buy Powers. To avoid this, you can use the Enhancement (ADEL File, pg 7, 1-6 pts) which provides a reserve of up to 6 points to buy Powers for the new forms.
First, there's the fact that most Powers have a visible effect (Mental Powers are a notable exception). This effect is up to the player to design. Nothing in the rules says that a change in form cannot be part of that effect. If all you want is a cosmetic change, go this route. Example: DC's Halo has six powers, one for each color of the rainbow, and her body glows according to which one she is using.
Obviously, there are also Powers that cause a physical change when used, like Growing or Stretching.
And then there's the "Instant Change" method. This Advantage says: "You can instantly transform from your secret id/normal mode to super mode." But what do these mean?
For most characters, "secret id" just means a change into costume (which begs the question, how long does it take to change into costume without this advantage- my guess is one Panel.) This does not prevent the use of the character's Powers unless it also has the Normal Disadvantage.
Super mode on the other hand, suggests a form with superhuman traits, such as Powers and Weaknesses. A player who gives its character this Advantage should be free to design such a form by buying such traits for it. Note that normal traits are still shared by both forms.
Presumably, you can also buy this Advantage more than once, with each giving you access to a different costume or super mode. In this case, the player can decide which form has which supertraits. He or she must still pay those traits' point costs of course.
Other traits that can be used for this purpose include:
Involuntary Change (UE pg 13) As above, but the change to and from super modes is triggered by something besides your will. The Narrator may give you a Mind Check to stop it.
Multiple Suits / Bodies (AP #2, pg 12) You can switch between them in-between Issues, assuming you have time to go back to your base. You can change suits / bodies during an issue, but doing so costs you a Hero Die. Each suit or body can have different powers, and when you put on a fresh one, it starts at 100 Hits.
Onerous Change (ADEL File, pg 6) You must roll a D6 when trying to change into Super mode; a 1-2 result indicate failure this Panel. Even if you succeed your powers will not activate until next Page.
Characters with the Obtrusive Disadvantage (ADEL File, pg 5) only suffer its effects in Super Mode.
A note on Alter Ego: This Advantage provides a second personality for the character, who may be helpful or unhelpful, may have separate skills, and even separate memories. The change between personas may also be intentional or triggered by something. It may be combined with any of the other options to create various form of shared-body characters.
Taking this Advantage more than once provides another extra personality each time.
Fusion: This variation, in which 2 or more characters combine to form a single one, is a popular option these days, thanks to shows like Dragon Ball and Steven Universe. To simulate it, simply add the Limitation "Requires X characters" to the appropriate Power, or specify the trigger for an Advantage or Disadvantage to be 'fusing with X persons'. Don't forget to give the super mode Alter Ego if the Fusion has more than one persona in control at a time.
