@panda1989 although switching schemes isn't common, it's not impossible - and there are a variety of reasons why a candidate would request this (made easier if there is ample time before the scheme begins). I think, to facilitate it properly, you need to be honest with the law firm about why it is you want to switch e.g. academic, personal circumstance, or competing internships.
I do think the latter isn't the most strongest, however, they will find out if the competing firm posts a LinkedIn picture of the cohort and your face/name is somewhere in there.
I'd be direct, and ask if there is any possibility for changing onto an alternative scheme, or if it's possible to be considered under a DTC as the situation as changed for XYZ reason. Reiterate your interest in the firm, and ensure them that they are still a top contender for you, but this is purely circumstantial.
Hopefully they respond with good news.