Adding external OCR text

Since the OCR function in Adobe Acrobat is not very good, I am looking at trying other OCR options out. However, while many of them seem to work better, they only produce editable text, but do not add it to the PDF.

So is there a way to add the text that I've OCRed elsewhere into a PDF using Adobe Acrobat, so that it still shows the original image, but allows me to highlight the text and copy/search it?