Apps and websites enable easier management of projects that involve a mix of internal and external people or that are composed solely of internal people.  Different pricing models are available.  Here are some tools that you might find useful:

Asana Project Management Tools.
Free and low cost versions are available.  Asana can also integrate over 100 other tools like MailChimp, EverNote, and GoogleSheets.

Basecamp Online Workspace.
Basecamp offers flat fee pricing, rather than per user pricing, and a non-profit discount.  Basecamp also has an automatic check-in prompt that reminds users to update statuses.

QuickBase Productivity Apps.
For institutions with truly specialized needs and an IT department, QuickBase enables you to build your own productivity/project management apps.  The company also provides its own productivity apps, so you don’t have to build your own.

Taskworld is a robust platform that focuses on larger corporate enterprises.  If you have a large institution with multiple different user groups, Taskworld could be your solution.

Each tool has its pros and cons.  They all focus on different audiences.  You might find that one tool works better for projects that include a lot of visuals.  Another tool may work better for projects that are primarily task-based.  Always pick the right tool for the job at hand.