Running Office 365 local app MS Project at the same time is a common need for many businesses. In order to accomplish this, you'll need to make sure that your system meets the System Requirements for Office 365 and that you are using the correct versions.
Once you've taken care of any potential compatibility issues, running both Office 365 and MS Project at the same time is relatively straightforward. You'll need to first open the Office 365 Local app and then open MS Project.
Once both are open, you can then begin using them side by side. You'll be able to copy and paste documents, images, or other files from one application to the other, then save or print the results accordingly.
To make sure your Office 365 local app and MS Project don't conflict, you should also check to make sure MS Project is set up to auto-save while open, and that you are regularly saving any open documents in Office 365 as well.
Finally, make sure to close both applications completely before exiting your computer, as leaving either one open can cause conflicts on restart. With these steps in mind, you'll be able to manage both applications successfully and get work done more efficiently.