  The discovered Higgs boson with a mass of 125 GeV exhibits properties which
are all in agreement with Standard Model predictions. However, the
corresponding measurements still allow for a considerable non-Standard Model
behavior of the h(125). Beyond Standard Model properties can show up in
non-Standard Model decays of the h(125) or in anomalous couplings of the Higgs
boson. This article presents four different analyses done at the CMS experiment
with 2012 and 2016 data that search for properties of the discovered Higgs
boson beyond the Standard Model. These include a search for lepton flavor
violating Higgs decays, a search for decays of the h(125) to light Higgs
bosons, a search for anomalous contributions to the Higgs trilinear
self-coupling, and finally a search for anomalous couplings of the h(125) to
vector bosons.
