Since you indicate more than one document, best approach is to define a new table linked to Contacts by ContactID where you have a single container field in each related record. A portal to this table can be placed on a contacts layout to list all attached files and where you can attach new ones as needed.
Such files can be inserted by reference or you can insert an actual copy of the file into the container. The choice is yours. Using by reference, the same copy of the file can be attached to multiple records and the size of your database file will not increase significantly with each attached file, and if you open a file, edit it and save it back to the hard drive, all records that link to it will link to the updated copy, but you then have to maintain these files in a directory where all users can access them and keep the file and folder names unchanged.
Either way, Export Field Contents, with the "Automatically open exported file" option selected can be used to open the file. If you write a script for this, it's possible to export the field to your user's temporary items folder and open it, though you then have to save "by reference" files back to their original location and it'd be easy for a user to save the file to the wrong location. On the other hand, if you save the file by reference, you can open it by double clicking it.