You can then ask once if the runner missed second, you can ask about third and home plate. You won't be able to ask about second base twice unless the umpire gets totally confused. A good umpire will, if needed, ask the crew for assistance before denying your appeal. If your team is unsure about which umpire was covering the base there is nothing stopping you from asking for help. In umpiring systems different plays bring about different base responsibilities.
Different crews approach the coverage of bases and tagups in unique formats.
The second case is less recoverable from. You wish to appeal a runner at first base but in doing so throw the ball wild, out of play. You have committed an error in the appeal. Even if you recovered the ball and tried again an umpire would have to deny the appeal. This is the textbook example of attempting a second appeal at the same runner at the same base.