Originally Posted by GuillaumeD

No, you don't. It is the OP's question.

It depends on the operating carrier policy.
I sumarized what I found on ST carriers website. Some of them say the extra allowance is also for ST E/E+ members but some do not. In the latter case, I specified the extra allowance for its own loyal customer. Finally, some airlines use piece and weight concept depending on the route.

Aeroflot: +1PC for E/E+
Aeromexico: +1PC 10kg max for E, +1PC 20kg max for E+ and other larger rules for specific dates and routes
Aireuropa: +1PC for FB Elite but nothing about ST E/E+
Airfrance: +1PC for E/E+
Alitalia: +1PC for its elite clients but nothing about ST E/E+
China Eastern: +10kg/+20kg for its elite clients
China Southern: 1PC or +10kg/+20kg (depending on the route lugage concept) for its elite customer
Czech Airlines: +1PC for ST E/E+
Delta: +1PC for ST E/E+ (23kg max in Y, 32kg in J)
KLM: +1PC for ST E/E+
Kenya Airways: nothing stated except on the FB part of the website
Korean Air: +1PC or +10kg/+20kg/+30kg for Morning Calm members
Tarom: +1PC for ST E/E+ members
Vietnam Airlines: +10kg/+15kg/+25kg or +0/+1/+1PC. The two first tiers are ST E but the first one doesn't allow you an extra bag. And, again, nothing written for ST E/E+


The list is not contractual and I am not responsible if there is a mistake, in any way. I decline all responsability if anything happens, even if your extra allowance is granted.
If you see a mistake, please tell me. If you experience it, let me know.