Do you switch between things in plural?
Solution 1:
Whether you switch brands or change trains, the idiom is pretty clear:
If the object changed is indeterminate, the plural is overwhelmingly preferred to the singular, by a factor of 25-40 to 1—doubtless because you are exchanging one brand/train for another.
In the rare case of a determinate object, however—if you change your train or they switch their brand—the plural vanishes and the singular rules.