stay with so or sth meaning

• [American slang]
  to remain in the company of someone or something.
    Please stay with me for a little while.
    How long did you stay with the company?

• stay abreast of so or sth:    [American slang]Go ...
• stay behind so or sth:    [American slang]Go ...
• stay by so or sth:    [American slang]to ...