I am not a big fan of making your web work only for a browser. We live in a BYOD era.
However, instead of target IE 11, you should rather target the features which IE 11 supports.
Look at the
www.caniuse.com[
^] and see what features are compatible with different browsers. It’s quite comprehensive.
Additionally, look at the
Modernizr [
^]library which can help you to test the features and implement a fall back in case required.