One may extend the Standard Model by adding the fourth generation of quarks and leptons. The behavior of the Higgs boson changes a little bit. Well, it changes substantially enough so that this Higgs boson in a larger model may be distinguished from the Higgs boson according to the Standard Model.
One may also modify the Standard Model in another way: make the Higgs boson fermiophobic. . . a fermiophobic Higgs boson is one that doesn't interact with the fermions (leptons and quarks) at the tree level (the fermion masses have to be produced more indirectly). The interactions with the W-bosons and Z-bosons are still essential for the consistency of the theory.
The recent paper has simply excluded both the four-generation interpretation of the newly found Higgs boson as well as the fermiophobic interpretation of the newly found Higgs boson. The confidence that these models – that are very specific, essentially as predictive as the Standard Model itself – have been falsified is very strong.
These results extend some previous 2012 results that have excluded the possibility that the 126 GeV Higgs boson is a pseudoscalar rather than a scalar; and that its spin is greater than zero such as J=2. Some deviations in the behavior of the Higgs boson from the Standard Model may be found in the near or distant future – at most something like 10% deviations in the coupling constants.The exclusion in the fourth generation case is really not just an exclusion of a different kind of Higgs boson, it is really a generalized exclusion of the Standard Model with four generations entirely. And, while the paper apparently does not rigorously examine the Standard Model with more than four generations, it is a fair assumption that those models would also contradict the Higgs boson data we have, just as the four generational model does. Thus, this is one more piece of very powerful evidence that the Standard Model has precisely three generations of fermions, no more and no less.
A fermiophobic Higgs boson was never something many people really expected.
Matt Strassler has recently discussed other ways that the detected particle could be discovered to be something other than a Standard Model Higgs boson.
Strassler also discusses what kinds of supersymmetry (aka SUSY) theories are and are not excluded by the increasingly precise data on the behavior of the Higgs boson. Minimal supersymmetry is pretty much dead, as are many other versions of these theories. But, there are enough moving parts in more complex SUSY theories that they can't be entirely excluded yet.