Great question! I work at Conga and have worked with quite a few customers to account for this requirement. If your workflow is to create and download a merged document, make changes to the doc, and then print it, then this is what I would suggest:
1) Use Conga Composer to merge your document and ensure that you're using a Microsoft Word template. Configure your merge process to keep the file in Word format (this is the default setting).
2) After using Composer to download the file, simply edit the file in Word just like a normal document.
3) Once you've made your changes, print the doc.
Does that type of workflow meet your needs? There are some other AppExchange apps that allow you to edit documents post-merge (Contractually, for example) but I've found that they're not really geared towards printing.
I hope this helps!