What you are trying to describe is what we call phase transition. So just to make it clear the reason higgs field working like that is that after the big bang and cooling of universe to about 10^5 kelvins (don't try to convert this to this strange unit of Fahrenheit) the field transitioned from high energy state to lower energy state. This is what gave rise to the higgs mechanism (what the article talks about).
Now this mechanism is responsible for the electroweak symmetry breaking, could it be others? Yes many think so. A lot of grand unification theories (GUTs) predict existence of some. The most famous one is Supersymmetry. There is a term called GUT phase transition that describes these fields.
Well another particular similar field would be what cosmology people call the inflaton. It is hypothesized that it has driven the expansion of the universe during the inflation event. But that cannot be repeated because it needs much higher energy state that it cannot be happening again.
But some theories of dark matter involve fields that could still be in a symmetric state (like higgs before phase transition) and that these fields would undergo a phase transition that we can see some observation like changes in dark matter distribution.
There is the concept of late dark matter symmetry and false vaccum decay (an idea that we are actually in a local minimum and that the true absolute point is not reached yet. If this is true it would be interested as if we reached this point then laws of physics will change (not our understanding but literally the laws will change). This could lead to a changes in particles properties, masses and forces. This could even change the structure of the space-time itself. This transition will be interesting because it could propagate as a bubble through the universe at speed of light. It seems more on a verge of science fiction but there is a theory behind that [1]
[1] https://en.m.wikipedia.org/wiki/False_vacuum