Forever Testing has 4 distinct storylines, one for each map in the mod, as follows:
"Once in a blue moon"
Sometime after the events of Portal 2, Chell travels to outer space to seek reconciliation with an old friend.
"On the shoulders of giants"
In an unknown time during the 90s, a lone test subject undergoes a test, supervised by an uncanny Cave Johnson voice with a newly found, oddly empathetic attitude towards cubes.
"A short break"
Set during Portal 2's campaign, GLaDOS begrudgingly allows chell to ride an elevator up to the surface mid-test, but not without maintaining an attentive watch over her.
"Autoportal Fling"
In an alternate universe where aperture uses somewhat different test chamber design principles, an un-named test-subject, #865, runs a simple test involving automatic portals.