MacOS – My screen isn’t working, how can I connect to an external monitor

Officially, Apple reports that the Retina Display MacBook Pro models can support two external displays up to a 2560x1600 resolution via the Thunderbolt or Thunderbolt 2 ports or one display with a maximum resolution of 2560x1600 via Thunderbolt and one display up to a maximum resolution of 1920x1200 (1080p) via HDMI.

http://support.apple.com/kb/SP690

MacBook Pro (Retina, 15-inch, Late 2013) - Technical Specifications. Display. Retina display: 15.4-inch (diagonal) LED-backlit display with IPS technology; ... on the built-in display and up to 2560 by 1600 pixels on up to two external displays, ..

Mavericks has been know to have some issues with external monitor, most of it was fixed in the 10.9.3.

Set your monitors to correct resolution and try again.

There's a Ruby script here:

https://gist.github.com/bastibense/6549835

#!/usr/bin/ruby
# Create display override file to force Mac OS X to use RGB mode for Display
# see http://embdev.net/topic/284710
# 
# Update 2013-06-24: added -w0 option to prevent truncated lines

require 'base64'

data=`ioreg -l -w0 -d0 -r -c AppleDisplay`

edid_hex=data.match(/IODisplayEDID.*?<([a-z0-9]+)>/i)[1]
vendorid=data.match(/DisplayVendorID.*?([0-9]+)/i)[1].to_i
productid=data.match(/DisplayProductID.*?([0-9]+)/i)[1].to_i

puts "found display: vendorid #{vendorid}, productid #{productid}, EDID:\n#{edid_hex}"

bytes=edid_hex.scan(/../).map{|x|Integer("0x#{x}")}.flatten

puts "Setting color support to RGB 4:4:4 only"
bytes[24] &= ~(0b11000)

puts "Number of extension blocks: #{bytes[126]}"
puts "removing extension block"
bytes = bytes[0..127]
bytes[126] = 0

bytes[127] = (0x100-(bytes[0..126].reduce(:+) % 256)) % 256
puts 
puts "Recalculated checksum: 0x%x" % bytes[127]
puts "new EDID:\n#{bytes.map{|b|"%02X"%b}.join}"

Dir.mkdir("DisplayVendorID-%x" % vendorid) rescue nil
f = File.open("DisplayVendorID-%x/DisplayProductID-%x" % [vendorid, productid], 'w')
f.write '<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">'
f.write "
<dict>
  <key>DisplayProductName</key>
  <string>Display with forced RGB mode (EDID override)</string>
  <key>IODisplayEDID</key>
  <data>#{Base64.encode64(bytes.pack('C*'))}</data>
  <key>DisplayVendorID</key>
  <integer>#{vendorid}</integer>
  <key>DisplayProductID</key>
  <integer>#{productid}</integer>
</dict>
</plist>"
f.close

You'll have to run it in El Capitan's rootless mode for it to work.