Molecule or molecular ion that spontaneously breaks up in two different ways
This happens all of the time in mass spectrometry following electron-impact ionization. Following ionization, each molecular ion decomposes (or fragments, to use mass spectrometry lingo) into other radicals and ions, usually following multiple pathways. As the pressure inside a mass analyzer is usually near vacuum, each fragmentation event is independent. No collisions or reactions between particles occur. The mass analyzer collects all of the fragments and generates signal that computer software converts to a mass spectrum - a frequency bar graph of the masses of species generated. For some very simple molecules, only one fragmentation pathway may predominate, but for most organic compounds, there are multiple fragmentation pathways. 

For example, let's consider the fragmentation of but-3-en-2-one radical cation with the formula of $\ce{C4H6O+}$ and the structure shown below. The mass/charge ratio (m/z) is 70 for this compounds 



There are at least two different fragmentation pathways. 

The first fragmentation pathway is a loss of a vinyl group ($-\ce{C2H3}$, -27 m/z):
$$\ce{C4H6O+ -&gt; C2H3O+ + C2H3 }$$



The second pathway is a loss of a methyl group ($-\ce{CH3}$, -15 m/z):
$$\ce{C4H6O+ -&gt; C3H3O+ + CH3}$$



Each of these fragmentation pathways is independent. Here is a copy of the mass spectrum from the NIST Chemical Webbook, which is a frequency bar graph of all possible fragments. You can see in addition to the two pathways mentioned above, there are many other possible fragments.



We can estimate the relative rates of these processes from the frequencies of the peaks in the mass spectrum. The first pathway occurs with a relative frequency of 83.19 (based on the height of the m/z = 43 peak) , and the second pathway occurs with a relative frequency of 1.000 (from the height of the m/z= 55 peak). We can use these as proxy for the relative rates of decomposition. We can also see that the parent ion survives this process with a relative frequency of 0.57779 (from the m/z = 70 peak), which indicates that the parent ion has at least some stability.