Hello
In most cases you can use στηρίζω and υποστηρίζω interchangeably. However the “υπο” prefix in "υπο-στηρίζω" gives a meaning of “little”. So “στηρίζω” means that I support, while "υποστηρίζω" means I do support, but to a lesser extent.
Example:
Υποστηρίζω την ομάδα μου, θέλω να νικήσει στον αγώνα = I support my team, I want her to win the game.
Στηρίζω την ομάδα, έχω δωρίσει 300.000 ευρώ για να χτιστεί ένα στάδιο = I support the team, I have donated 100.000 euros to build a new stadium.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.