You can upgrade MacBook 2013/2014 with NVME drive (sort of) but you’ll meet few problems after that.
First of all you have to upgrade your MacBook EFI by installing High Sierra, then you can attach NVME drive with adapter and it should be recognizable.
Problems you might have:
- Long time before boot (even if disk is set as bootdrive)
- Finder shows it as external
- Random freezes or restarts after hibernation
Your only option is to use SM951 AHCI (PCIe/mSATA instead of PCIe/NVMe) drive - MZHPV128/256/512 This one works as it should.
MacBook Pro/Air 2015 has no problem with M.2 PCIe/NVMe drives and you can upgrade it safe and works great ;)
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