Is it possible to get an extension for my transition fill?

Yes - but only in specific circumstances. Your Medicare Part D plan may provide you with a transition fill extension. However, such an extension is provided only on a case-by-case basis in exceptional situations such as when you have filed a formulary excepting request that has not been processed by the end of your transition fill period.

And as reference, please see:

The Centers for Medicare and Medicaid Services (CMS') Medicare Prescription Drug Benefit Manual, Chapter 6 – Part D Drugs and Formulary Requirements, Section 30.4 - Transition, (Rev. 18, Issued: 01-15-16, Effective: 01-15-16; Implementation: 01-15-16):

Section 30.4.4.3 - Transition Extension

"A Part D sponsor may need to make arrangements to continue to provide necessary drugs to an enrollee via an extension of the transition period, on a case-by-case basis, to the extent that his or her exception request or appeal has not been processed by the end of the minimum transition period.

It is vital that sponsors give affected enrollees clear guidance regarding how to proceed after a temporary fill is provided, so that an appropriate and meaningful transition can be effectuated by the end of the transition period. Until that transition is actually made, however, either through a switch to an appropriate formulary drug, or a decision is made regarding an exception request, continuation of drug coverage is necessary, other than for drugs not covered under Part D." [emphasis added]

Your Medicare Part D drug plan will also provide an Emergency Supply of Part D medications in long-term care settings. You can refer to your plan documentation and find information such as:

"Emergency Supply for Long-Term Care Residents - In the long-term care setting, after the transition period has expired, [the Medicare drug plan's] transition policy provides for a 31-day emergency supply of non-formulary Part D drugs or formulary Part D drugs that require prior authorization, or step therapy and/or have quantity limits (unless the enrollee presents with a prescription written for less than 31 days) while an exception or prior authorization is requested. Greater than a 31-day supply will be provided when the drug is prepackaged and cannot be dispensed at a lower day supply."