I too have n56jr. I have managed to install 10.9.0 (and upgrade to 10.9.2) but only with chameleon not with clover uefi. Also, I use a patched Haswell kernel. To boot the installer I had to delete all NV*.kext from the /S/L/E of the install usb.
Got working: touch pad, ehernet/Apple store (RealtekRTL8111), keyboard,audio (VoodooHDA),display in VGA mode (i had to remove all AppleIntelHD3/4/5*.kext and NV*.kext to be able to boot).
Not working: AirPort (got Intel Dual Band Wireless-N 7260 buried somewhere deep in the laptop chassis), Intel Graphics HD 4600M (and of course GeForce GTX 760M).
What has to be done:
1. Boot and install OS X with Clover UEFI (I want a dual boot laptop). So far, clover fails at loading graphics - seams like it is trying lo load NVidia kexts no matter what is in config.plist. I have tried to create a DSDT of n56jr using all available tools and methods but the extracted ACPI file fails to compile (there is a sequence of zeros in the file).
2. Enable integrated graphics HD 4600M (80860416) as stated above i cannot patch it in DSDT only tried boot option IGPlatformID.
Any guru help will be appreciated.