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Each level of building takes 1 field. If you ran out of fields, you can't build more levels on that planet. And if you need more you could buy with nano.
Of course you are not obligate to use nano. You can delete that planet and colonise new one and hope that it will have more available fields.
And for last nano can be received buy paying for it, or if someone shares own nanos with you...

Just to add something - if you don't want to use nanocredits for expanding the fields on your planets - try to colonize on planets with coordinates larger than *:*:11. It gives you greater chance of obtaining high fields planet. And also... If you are not going to be a strong farmer, but you play as an attacker (i.e. you don't plan to go for 30th lvl mines) - you won't need that many fields anyway.