Can anyone give me an example of a sentence or phrase in which it is possible to change which words are pluralized yet is still makes sense?
You could use a noun which is its own plural:
The sheep is happy.
The sheep are happy.
Or you could use the subjunctive, which in English is the same for singular and plural nouns:
If I were concrete, you'd walk all over me.
If they were concrete, you'd walk all over them.
Or you could just change the direct object's plurality, and thus not need to worry about subject-verb agreement.
I love the cat.
I love the cats.
Interesting question. Although the meanings could alter slightly, how about:
The peaks of the mountain are majestic. vs. The peak of the mountains is majestic.
Of course, the verb has to change here. Say we're talking the Himalayas. There are multiple connected mountains, but whether using singular or plural doesn't alter the meaning of the mountain range known as the Himalayas. The same is true of the peaks. Although there is an apex, to use "peak" could also mean the series of extremely high elevations that surround the apex. "The peak of the mountain" (both singular) would definitively label the apex.