You're a time traveler, but an unwilling one. You have an odd clockwork "mark" on your hand that not only pulls you through time but gives you strange abilities. You time travel by jumping into one of your past lives, inhabiting their place temporarily to fix a paradox. The paradox alters everyone's perception so you'll still look like the real "you", but no one will seem to notice a difference.
For example, if you were Abraham Lincoln in a past life and traveled back in time to take his place...Abraham Lincoln would look just like you and everyone would act like he ALWAYS looked like you. That is until you finish the job and move onto the next disaster.
You always have a partner who shows up in the paradox first to investigate the crime. If it's something that needs the two of you (which is usually the case), you'll get pulled in as backup.
Someone who doesn't belong in the time you've been thrown into has committed a crime that never should have happened. It has created a paradox and time is slowly falling apart. A paradox is an open wound in time and as it festers, awful, unmentionable things start to get in.
You've got to solve the crime, find the person who doesn't belong, and send them back to their own time. If you fail, time gets broken and you start all over. If one of you dies...you start all over. Time will keep skipping like a broken record until you get it right...or reality completely crumbles. No pressure!