The Cape Verdean registry office is asking me for an "original" of my birth certificate, for more than one process. As a US citizen, this is a fairly expensive document to get! (It would currently cost $45 each for me, not including shipping costs, from VitalCheck.) Is there some way around this requirement, other than ordering and paying for multiple birth certificates to be shipped from the US? Is it worth it to plead with the workers to give me the certificate back afterwards, so I can use it in another process (or just keep it for myself)?
Use certified copies
You probably won't get very far trying to get your certificate back afterwards. They probably need to keep this in the permanent file.
In Cape Verde, what they call an "original" birth certificate is a document that costs 150$00 and is printed on-demand. Unlike birth certificates in some countries like the United States, these documents have an expiration date. They contain additional information unrelated to birth, such as marriages and name changes, in an "Annotations" section. This might be why they don't think twice about asking you for an original birth certificate.
The good news is that, for any process that requires an "original" birth certificate, you should be able to submit a certified copy of it. You can get certified copies of most any document at the local Notary Office; this costs only 550$00 per document (not per page). As is the norm in Cape Verde, you must bring the photocopy to them; they won't make the photocopy there.
The bad news is that foreign birth certificates used in Cape Verde are treated as having an expiration date of 6 months after they're emitted, even if they'd be valid longer in the country they're from.
Don't forget that you will have to have the document translated, since it's not written in Portuguese. Also, for some processes, such as marriage, your birth certificate can't come directly from the US to Cape Verde. It must first be authenticated at the Cape Verdean Embassy, in Washington, D.C., or the Consulate in Boston. They will staple an additional page to it stating that they have found it to be authentic. You can then create certified copies of the entire document (certificate + authentication) in Cape Verde.