I have a sentence: However, in other departments, the options have ___ greatly. What would fit 'options' in this case: stretched, protracted, widned or lengthened and why?
Are there any collocations with these verbs and/or with options?
Thanks in advance!

Why don't you use 'opportunities have greatly/considerably increased'?
"strech" is used for instance as "strech the facts too wide" and would need an addition like "streched to include/cover ... opportunities."
Other candidates 'protracted, widned or lengthened' have unnecessary connotations. Keep things simple. .

А что делать, если это предложение из учебника и ей нужно только вставить наиболее подходящее слово? Посоветуйте авторам учебников to keep things simple.
Автору: мне кажется widened подходит лучше всего.

I can't, it is an exercise on verbs.
I am searching for contexts or collocations of these verbs, which would/or wouldn't fit stylistically and grammatically.

But thank You anyway

Bingo!
And why does 'widened' fit? I also thought of this word, but I can't say why others DON'T fit.
My dictionaries cannot give me any reason Don't You know where I could look it up?
Thank You!

'Widened' is a more neutral word and suits better if you want to say that the array of opportunies has increased. I haven't realized that this question comes from a test or exercise. "Prolong" has connotations of time, while protracted - also a meaning of time or measures/facts protracted/stretched in time or space, however they say nothing about growing opportunities.