Need more auto-connection points on Visio shapes

On the Home tab, in the Tools section, you should have a 'Connection Point' command (shift+control+1). Select your shape, click the command, then hold down the control key and left click where you want to add, move, or delete a connection point.

I found the point and click method for adding new connection points to be a bit clumsy so I prefer: Right click on shape -> Show ShapeSheet. You can then edit the Connection Points table directly and ensure that your connectors are exactly where you want them.

For those who can't find the Show ShapeSheet option: since Visio 2010 you have to enable developer functionality through the Custimize Ribbon option to use the ShapeSheet. More info: https://support.office.com/en-us/article/What-happened-to-the-ShapeSheet-18505403-6934-438d-b40e-ec32c89a979a.