How to upgrade gnu make in OS X El Capitan Currently I am at:

mhoggan-C02S81PRG8WM:c_velodyne mhoggan$ make --version
GNU Make 3.81
Copyright (C) 2006 Free Software Foundation, Inc. This is free
software; see the source for copying conditions. There is NO warranty;
not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

This program built for i386-apple-darwin11.3.0
mhoggan-C02S81PRG8WM:c_velodyne mhoggan$ make --version GNU Make 3.81
Copyright (C) 2006 Free Software Foundation, Inc. This is free
software; see the source for copying conditions. There is NO warranty;
not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

This program built for i386-apple-darwin11.3.0


Is there a way with Homebrew to upgrade to 4.1 or 4.2?
Yes, you can run:

brew install homebrew/core/make


on earlier systems this was:

brew install homebrew/dupes/make


This will install make 4.2.1.

Another option, if you want to retain the system installed make version, is to install remake instead.

brew install remake