Yes.  The Centers for Medicare & Medicaid Services (CMS) provide case-by-case Special Enrollment Periods allowing a person to change Medicare Part D or Medicare Advantage plans outside of the annual Open Enrollment Period based on exceptional or extraordinary circumstances (the annual Open Enrollment Period or AEP begins October 15 and continues only through December 7).

As guidance, the CMS Medicare Part D and Medicare Advantage plan Manuals include sections for "SEPs for Exceptional Conditions" specifically addressing extraordinary SEPs that are considered by CMS representatives on an individual basis and note:

"CMS has the legal authority to establish SEPs when an individual or group of individuals meets exceptional conditions specified by CMS, including [SEPs] on a case-by-case basis."

Under the section of "SEPs for Exceptional Conditions", CMS lists the following established 20 established "exceptional" SEPs:

1. SEP EGHP (Employer/Union Group Health Plan)
2. SEP for Individuals Who Disenroll in Connection with a CMS Sanction
3. SEP for Individuals Enrolled in Cost Plans that are Non-renewing their Contracts
4. SEP for Individuals in the Program of All-inclusive Care for the Elderly (PACE)
5. SEP for Institutionalized Individuals
6. SEP for Individuals Who Enroll in Part B during the Part B General Enrollment Period (GEP)
7. SEP for Individuals Who Gain, Lose, or Have a Change in their Dual or LIS-Eligible Status
8. Part D SEPs to Coordinate With MA Enrollment Periods
9. SEP for Individuals who belong to a Qualified SPAP or who lose SPAP eligibility
10. SEP for Disenrollment from Part D to Enroll in or Maintain Other Creditable Coverage
11. SEP for Individuals disenrolling from a Cost plan who also had the Cost plan optional supplemental Part D benefit
12. SEP to Enroll in an MA Plan, PDP or Cost Plan With a Plan Performance Rating of Five (5) Stars
13. SEP for Non-U.S. Citizens who become Lawfully Present
14. SEP for CMS and State-Initiated Enrollments
15. SEP for Providing Individuals Who Requested Materials in Accessible Formats Equal Time to Make Enrollment Decisions
16. SEP for Government Entity-Declared Disaster or Other Emergency
17. SEP for Individuals Enrolled in a Plan Placed in Receivership
18. SEP for Individuals Enrolled in a Plan That Has Been Identified by CMS as a Consistent Poor Performer
19. SEP for Individuals Who Enroll in Medicare premium-Part A or Part B using an Exceptional
Condition SEP, as Described in 42 CFR Parts 406.27 and 407.23

And the last Special Enrollment Period in this section, "20. SEP for Other Exceptional Circumstances", offers even broader guidance for granting an SEP in extraordinary situations:

CMS will establish an SEP, on a case by case basis, for individuals whom CMS determines have experienced exceptional circumstances related to enrollments into or disenrollments from Part D plan that are not otherwise captured in regulation. Consistent with current practice, CMS will consider granting an enrollment or disenrollment opportunity in situations such as the following:

• Circumstances beyond the beneficiary’s control that prevented them from submitting a timely request to enroll or disenroll from a plan during a valid election period. This is inclusive of, but not limited to, a serious medical emergency of the beneficiary or his or her authorized representative during an entire election period, a change in hospice status, or mailed enrollment or disenrollment requests returned as undeliverable on or after the last day of an enrollment period.

• Situations in which a beneficiary provides a verbal or written allegation that his or her enrollment in a MA or Part D plan was based upon misleading or incorrect information provided by a plan representative or State Health Insurance Assistance Program (SHIP) counselor, including situations where a beneficiary states that they were enrolled into a plan without his or her knowledge or consent, and requests cancellation of the enrollment or disenrollment from the plan.

• A SEP may be warranted to ensure beneficiary access to services and where without the approval of an enrollment exception, there could be adverse health consequences for the beneficiary. This is inclusive of, but not limited to, maintaining continuity of care for a chronic condition and preventing an interruption in treatment.

CMS will review supporting details and documentation to determine eligibility for the SEP for exceptional circumstances. CMS’ review can be in response to an individual beneficiary’s request for an exception to the current enrollment rules, as well as CMS’ determination that an exception is warranted for a group of beneficiaries.

The SEP would take effect once CMS makes its determination and the enrollee has been notified. The effective date for an enrollment or disenrollment election using an approved enrollment exception would be based on the beneficiary’s circumstances and may be either prospective or retroactive." [highlighting and emphasis added]

More from CMS about this "exceptional" SEP

A CMS blog published back on November 27, 2019, entitled, "We’re Heading into the Last Week of Medicare Open Enrollment Don’t Miss Out on Your Chance to Find Better Coverage" also addresses the issue of a discretionary Special Enrollment Period (SEP) that was available in extraordinary circumstances where people relied on false or misleading information when making an enrollment decision:
"Of course we want to ensure that beneficiaries are confident in their decisions and happy with the coverage they choose. We have protections such as Special Enrollment Periods in place if something happens to shake that confidence. As is the case every year, our call center representatives and staff caseworkers can help beneficiaries throughout the year if they believe they made the wrong plan choice because of inaccurate or misleading information. This process isn’t new, but this year we’re doubling down on ensuring that it’s a simple and painless experience for beneficiaries. Our staff is trained and ready to help any beneficiary who needs it. All they need to do is call 1-800 MEDICARE. Again, we’ve always had a Special Enrollment Period for people who think they made a wrong choice due to inaccurate information." [emphasis added]

Question: How can I get this "exceptional" SEP so I can Medicare plans outside of the AEP?

Medicare beneficiaries should contact a CMS representative (by calling 1-800-633-4227) with any questions and to learn whether Medicare will grant this SEP based on their specific situation or circumstances.

Please remember that SEPs for extraordinary situations are granted on a case-by-case basis and depend on the facts surrounding your enrollment experience, so please be sure to provide the Medicare representative with as much information as possible – especially if your lack of Medicare plan coverage could adversely affect your health (for example, you suffer from a chronic health condition and rely on the continuous care and medications provided by your Medicare plan).

References:

Medicare Prescription Drug Benefit Manual, Chapter 3 - Eligibility, Enrollment and Disenrollment, p. 34, 121, Updated: August 19, 2011 (Revised: November 16, 2011, August 7, 2012, August 30, 2013, August 30, 2014, July 6, 2015, September 1, 2015, September 14, 2015, December 30, 2015, May 27, 2016, August 25, 2016, June 15, 2017, July 31, 2018, August 12, 2020, & August 15, 2023))

Medicare Managed Care Manual Chapter 2 - Medicare Advantage Enrollment and Disenrollment Updated: August 19, 2011 (Revised: November 16, 2011, August 7, 2012, August 30, 2013, August 14, 2014, July 6, 2015, September 1, 2015, September 14, 2015, December 30, 2015,May 27, 2016, August 25, 2016, June 15, 2017, July 31, 2018, August 12, 2020, & August 15, 2023)

See the related Frequently Asked Question (FAQ: "Can I change Medicare plans more than once during a Special Enrollment Period (SEP)?"

Medicare Blog: https://www.cms.gov/blog/were-heading-last-week-medicare-open-enrollment-dont-miss-out-your-chance-find-better-coverage (now offline 12/15/2021, but available in internet archive).