Data entry form for department use but limited use database

[clew3]

I have an Access database that is currently housed on a shared network drive that only allows two people permission to access. However, I want a form that anyone in the department could use to add new records to one table of the database. Ideally, the form would be located on a SharePoint site page, but this is not a necessity. Currently, I have connected the table to a SharePoint list and allowed access to the SharePoint form. However, since it is a relational table, the SharePoint list isn't an ideal option due to limitations. Is there another way to accomplish this? I can use SharePoint 2013, SharePoint Designer 2013, InfoPath 2013, and Access 2013. Any ideas are appreciated because I'm stumped.

Edit: the database doesn't have to stay on the network drive, it can be moved somewhere else (publishing it to SharePoint for example) as long as it can remain secure with built in user permissions.

[NTC]

An Access database is inherently fully multi user - assuming it is installed correctly. It is referred to as a split database, and consists of 2 files - a single back end file that contains the tables only - and a front end file which is copied as many times as needed so each user has one. You do not need to have the back end tables as SharePoint Lists - although you can without any problem. Every user must have Access on their PC and be linking to the back end tables.

It is not at all uncommon for the front end file to differ depending on the 'class of user'. For instance the executive management may have a front end that has lots of reports and visibility into data while the front end for the data entry staff may just have a couple of forms specific to their daily task. They all link to the same back end file of tables. One can implement the differing front ends either by literally making different front end files - or - by making a single front end file but manipulating visibility of features dependent upon a log-in which identifies the user's class.