The term "managements" can cater to a great pool of end users dealing with product management, reputation management, wealth management, management degree etc
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No self respecting company will use such name. Words like managements, informations, purchasings, bettings are incorrect and awkward. Maybe as .com someone would want it for up to $1000, but as .co I believe it has no value.
You are correct in that (i think) but @tupungato is also correct.
The plural does not really work in this instance. An example where it may work is drone/drones, airplane/airplanes, hit/hits. I don't know what the correct term is for how a plural will change a word from a noun to pronoun or pronoun to noun or adjective to pronoun and all that but there are many instances where it would be a less than desirable domain name and management/managements is one of them. Another would be spend/spends or acquire/acquires.
I actually not so certain managements is really a noun. Agency/Agencies would be a better example of a noun and that would be an example, (in my opinion) of something more desirable. I hope that helps and doesn't make things too confusing.