Opening multiple instances of ArcGIS Pro?

At this time, no, you cannot open multiple instances of Pro on the same machine. You can open Pro on different machines (up to 3) with the same named user as long as the license has not been taken offline.

Idea: Two ArcGIS Pro Maps Open at the Same Time

ArcGIS Pro 2.0 has just been released yesterday.

I tried it briefly this morning and found that it will in fact allow multiple instances to be opened.

So while it was not possible to open multiple instances with ArcGIS Pro 1.x, it is possible to do so using 2.x.

Here is a screenshot of my laptop with 4 ArcGIS Pro instances running

See What's new in ArcGIS Pro 2.0

• You can now open and run multiple instances of ArcGIS Pro at the same time. Work on multiple projects simultaneously and open a new or existing project without closing your current project.
• The same project can be opened several times. The first time a project is opened, ArcGIS Pro will have a writable copy of the project. All other instances of the project will be read-only. You can work with a read-only project in the same manner as if the project is writable; however, on saving your changes you will see the Save Project As dialog box. Save a copy of the current project file (.aprx) to a writable location if you want to keep your changes. Learn more about opening and saving projects.

You should be able to auto-update from 1.x to 2.0 from within the ArcGIS Pro application. If it doesn't give a pop-up saying a new version is available, you can go to the Application menu > About and check for updates.