How can I “magnify” a PDF document with DIN A4 pages to another one with DIN A3 pages?

Use Adobe Reader for that (here on Linux, but you could use another free Ghostscript based destiller on Windows, e.g. the PDF pseudo printer PrimoPDF).

1. Open the document in Adobe Reader.
2. Open the dialog “File -> Print …”.
3. Select the printer “Custom …”, and in the combobox that appears at the right border of the dialog, select DIN A3 as paper size (you could also enter 420x297mm as custom paper size for this printer, or use a physical printer with both modes).
4. Select “Page scaling: Fit to printable area”, and if necessary “Auto Rotate and Center”.
5. Select “Print to file”, and select a file to print to.
6. Press “OK”.
7. The resulting file is a postscript file. The page size of a postscript file can be auto detected, or manually set. Here, re-destilling to PDF with ps2pdf gets the page size wrong (it uses DIN A4). Therefore, open the document in kghostview and print it from there to a PDF file (it has correct page size auto detection, see the menus).

One can probably use ps2pdf when telling it about the desired page size explicitly, but I haven’t tested that yet:

ps2pdf -sPAPERSIZE=a3 file.ps