Can you upgrade stadium facilities from level 2 to level 6 right away, or you should build it level by level?
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Right away... if you have the money :junior:

Ok. But when I click to extend it to level 4 for youth training grounds (more talented players sign up?), and go to some else menu, when I get back to club facilities, youth training grounds are marked as "in building" and description is 20% less dropouts (like level 2).

hope it bug in description, not in effect.

this is my first time to run my own club, so I dont want to screw something up.

Probably its showing which Training Ground do you have actually (level 2)...

but it also shows how many weeks left for the new construction to be ready (level 4)

No, it shows next level.
Construction will last 90 weeks ...

Maybe after eg.20 weeks (which is needed for next level) it will show description of level 3???