I use Microsoft 365 at work (provided by employer). I wish to have my own personal, separate 365--is that possible?

Yes.

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You will have 2 office installations. The "business" one and a new "consumer" one.

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Before you buy, check to see if your school qualifies for the "HUP", Home Use Program. It costs the school nothing. It gives you a 30% discount on your subscription.

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You can set up one or both accounts to allow you to access the OneDrive for the other easily.

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If you are planing on consumer 365 rather than OneTime payment Office 2021, contact your family and friends to see if anyone already has 365 Family or 365 Personal (that they are willing to upgrade to 365 Family). 365 Family allows the owner to "share" a fully independent 365 license with up to 5 other people. Even the cost of 2 people sharing 365 Family will save each of them $20 per year. Price goes down to $16.67 each per year for a 6 way split on the cost.

HUP– Home Use Program- H.U.P.

If you work at a large company that has lots of 365 Business subscriptions, or you know someone who works in a place like that, you may qualify for the HUP, Home Use Program, discount. That is 30% off on price of a 365 Family/Personal subscription. It’s actually a good deal.
.Note: HUP requires you turn on the “Recurring Billing” feature to continue getting the 30% discount every year. Recurring Billing allows you to continue using the HUP even after you leave the company.
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HUP Propaganda:
https://www.microsoft.com/en-gb/home-use-program/resources
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Microsoft Home Use Program FAQ https://www.microsoft.com/en-us/home-use-program/frequently-asked-questions .

Check HUP Eligibility: https://www.microsoft.com/en-us/home-use-program?rtc=1
you submit your work/school email to check eligibility,
but you MUST use your "personal" email to activate the HUP subscription.
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Who qualifies ( https://www.microsoft.com/en-ca/home-use-program/resources ):
For employees to take advantage of the Microsoft Home Use Program discount, they need a valid corporate email address and an active Microsoft account, and the organization will need to meet one of the following criteria:
.  *  Customers who have active Software Assurance for qualifying Office applications.
.  *  Customers who have Microsoft 365/ Microsoft 365 E3/E5 from Software Assurance.
.  *  Commercial and government customers who have purchased 2,000 licenses or more of one or a mix of  Microsoft 365 E3 or E5.
.  *  Commercial and government customers who have spent $250,000 USD or more in the previous 12 months on eligible Power BI, Office, Surface devices and accessories, Windows and Enterprise Mobility.
.  *  Education and non-profit customers
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Install or reinstall through HUP
https://support.microsoft.com/en-us/office/install-or-reinstall-office-through-microsoft-hup-d99c6e4a-6756-4ece-99a0-b1df654ec7d3
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Activate HUP: https://support.microsoft.com/office/activate-o...
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Microsoft Home Use Program - Order History: https://www.microsoft.com/en-us/home-use-program/order-history .
If you purchased
   Office Professional Plus 2013/2016/2019,
   Office Home & Business for Mac 2016/2019,
   Visio Professional 2013/2016/2019, or
   Project Professional 2013/2016/2019
prior to November 30,2018, you can use the field above to request your installation information and product key(s).
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To do so, enter the work email address you previously used to make a purchase. Once submitted, we’ll confirm your purchase and send your installation link and product key to the email address you entered. Please note that you must still work at the same company from which you received the Home Use Program discount.
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If you purchased from the Home Use Program (HUP) after November 30, 2018, you can access your order history for those products on the 
Microsoft account, Services & subscriptions  https://account.microsoft.com/services/
page where you will sign in using the “personal” Microsoft account used to complete your purchase (not your work email).
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Troubleshoot HUP: https://support.microsoft.com/en-us/office/get-help-installing-office-through-microsoft-hup-f682c420-ed43-42d9-96e4-235dd7708848#BKMK_HUPKey
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Expired: HUP Sale Jan-Feb 2022 – Rare as Hen’s teeth

https://www.microsoft.com/en-us/home-use-program?ocid=eml_hup_cons_store_acq_officehup_m365_surface  (downloaded)

<snip>

Save 40% until February 23*

Microsoft 365 Family and Personal annual subscriptions are 40% off on your first year for Home Use Program eligible customers.*

</snip>.

Hello Raymond R,

Thank you for posting your question in our community, Yes you can have your own personal Office 365 account on the same computer. You just have to remember to sign into with the personal account when you want to use it. For example, in Excel or word you will see your username on the top right, just click on it and select sign in with a different account.

Best Regards, Asher