The question doesn't specify the language, so I'm adding an answer using C#; this works for me. I'm creating three separate but related PDFs then combining them into one.
After creating the three separate PDF docs and adding data to them, I combine them this way:
PdfDocument pdfCombined = new PdfDocument(new PdfWriter(destCombined));
PdfMerger merger = new PdfMerger(pdfCombined);
PdfDocument pdfReaderExecSumm = new PdfDocument(new PdfReader(destExecSumm));
merger.Merge(pdfReaderExecSumm, 1, pdfReaderExecSumm.GetNumberOfPages());
PdfDocument pdfReaderPhrases = new PdfDocument(new PdfReader(destPhrases));
merger.Merge(pdfReaderPhrases, 1, pdfReaderPhrases.GetNumberOfPages());
PdfDocument pdfReaderUncommonWords = new PdfDocument(new PdfReader(destUncommonWords));
merger.Merge(pdfReaderUncommonWords, 1, pdfReaderUncommonWords.GetNumberOfPages());
pdfCombined.Close();
So the combined PDF is a PDFWriter type of PdfDocument, and the merged pieces parts are PdfReader types of PdfDocuments, and the PdfMerger is the glue that binds it all together.