Search field on all pages

I love the ability to search for an employee on the employee tab but would like the ability to do that even once I have gone into an employee record.  Right now, if I am making changes to an employee record and I have saved the changes, I need to click on the employee link and wait for it to load before being able to search for another employee and make changes there.

Additionally, I would like to be able to search for a team name rather than having to scroll through 3 pages of teams to find the one that I want.  Then, again, once I make the change, I have to click on the team link and repeat the process of searching through all of the pages

It is possible to have a team search box and an employee search box on every page?  Or maybe just a search box that regardless of what you are searching for it will find it?