This is perfectly fine.
The only thing you need to do is let the reader know that they have switched viewpoints. This is easily done by having the new viewpoint character look at or think of the previous viewpoint character.
A sentence like
John looks dead. or
I wish I knew where John is. makes it unmistakeably clear, that the person narrating is not John.
The last thing I saw before I fell to the floor unconscious was Sarah's frightened face.
John hit the floor hard. I rushed to him ...
The clarification may come at the beginning of the chapter – or later, if you want to play with reader expectation.
In The Kiss of Deception, Mary E. Pearson tells the story from the viewpoints of three characters, a princess, a prince, and an assassin. The princess fled an arranged marriage to the prince and lives anonymously in a village. The prince follows her and stays in the village anonymously, so find out why she spurned him. The assasin is there to kill her, but doesn't immediately fulfill his assignment. The princess doesn't know the true identity of the two men and thinks, they are just travellers. The reader knows the two men are a prince and an assassin, but the parts told from their viewpoints do not identify them. As a reader, you don't notice this at first, identifying one viewpoint with the prince and the other with the assassin, because of their thoughts and behavior. Only after some time do you learn that you were mistaken and that what you thought was the prince is in fact the assassin.
I found this very interesting, but also annoying. Nevertheless it is an example of not letting the reader know (immediately), which character the viewpoint has switched to.
A famous novel that is told from three first person viewpoints (and one third person) is William Faulkner's The Sound and the Fury, if you need evidence from the literary canon.