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My suggestion is to find a small or medium-sized company that has both clinic and acute care work, and apply for a clinic position. Avoid the large (MedQuist, Webmedx, Transcend-type) companies because they have too many chiefs. You need to find a company where the person who assigns the work handles both clinic and acute care accounts.
As often as you can, find acute care dictations (from other companies at MTTEST or other sites that have sample reports or if you have tapes from school that are acute care) and practice, practice, practice, so you get used to operative note, H&P, and discharge summary formats and terminology.
After you have been there for a couple of months and have proven that you can do 99% QA, let your lead or supervisor (whoever does the assignments) know that you are willing to help out if there is a backlog in acute care. Usually at the smaller companies, if TAT is in jeopardy, all they want is a body doing the transcription. If you have a good rapport with that person and have proven that you know how to research so that QA does not have to take a lot of time with you, they may throw you a few acute care reports.
Eventually, if you do well, they will probably give you more and more, until you can honestly put on your resume that you have acute care experience.
That is basically how I did it, but it was many, many years ago and companies were more willing to mentor Medical Transcriptionists then. But, it still could work today. Just be sure to ask during the interview if they have both clinic and acute care accounts and see what type of reaction you get from the recruiter.
Good luck to you.