As Michael says, there don't seem to be any serious possibilities for a symmetry breaking, however there are some possibilities for tunneling into a different vacuum state. Ironically this would probably be a symmetry restoration rather than a symmetry breaking.

You may have heard of the String Landscape. This is the idea that string theory allows many metastable solutions for the universe and we may be in one of those metastable states. It's possible that the universe could tunnel into a state where supersymmetry is unbroken and all the compact dimensions are fully extended.

Slightly less speculative is the suggestion that the electroweak vacuum may be unstable. This has been briefly discussed in Measured Higgs mass and vacuum stability, or see the paper by Alekhin, Djouadi and Moch.

As Michael says, there don't seem to be any serious possibilities for a symmetry breaking, however there are some possibilities for tunneling into a different vacuum state. Ironically this would probably be a symmetry restoration rather than a symmetry breaking.

You may have heard of the String Landscape. This is the idea that string theory allows many metastable solutions for the universe and we may be in one of those metastable states. It's possible that the universe could tunnel into a state where supersymmetry is unbroken and all the compact dimensions are fully extended.

Slightly less speculative is the suggestion that the electroweak vacuum may be unstable. This has been briefly discussed in Measured Higgs mass and vacuum stability, or see the paper by Alekhin, Djouadi and Moch.