Setting content-length if app doesn't know what it is (no replies)

Behind my web server is an application that doesn't include content-length
headers because it doesn't know what it is. I'm pretty sure this is an
application issue but I promised I'd come here and ask the question - is
there a way to have nginx buffer an entire server response and insert a
content-length header if none has been provided (i.e. by *-fpm, upstream
proxy, etc)?
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