Setting up one or the other is easy, but I can't seem to activate both at once.
Before anyone asks, my primary reason for wanting to do this is security.
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You can go trough Android's security using only one at once. For example, if you have both Fingerprint and Pattern activated, only one of them is required to unlock the device. However, with third party apps like Next Lock Screen or Picturesque Lock Screen, you can actually stack them. If you activate Next Lock Screen, Pattern and Fingerprint, you will have to use Next Lock Screen first, then either Pattern or Fingerprint.
@Susan If your phone is rooted and has the Xposed framework installed, you can take a look at MasterLock. It's nearly impossible to remove (installs as system app, is device admin, etc). Though, I can't resist to ask, why want to use two lock methods at once? Only you have your finger prints. An additional number lock seems kind of useless to me.