AA - Using AsiaMiles:
-AA flights in fare classes Y, B, and H are eligible for Economy to Business Class Upgrade Awards.
-AA flights in fare classes J, D, and I are eligible for Business Class to First Class Upgrade Awards.

BA - Using Executive Club Miles:
-No restrictions.

Using AsiaMiles:
-BA flights in fare classes Y, B, and H are eligible for Economy to Premium Economy Class Upgrade Awards.
-BA flights in fare classes W, T, and E are eligible for Premium Economy to Business Class Upgrade Awards.
-BA flights in fare classes J, C, D, I, and R are eligible for Business Class to First Class Upgrade Awards.
-Upgrade Award is not applicable for Economy to Business Class upgrade.

CX - Using AsiaMiles:
-CX & KA flights in fare classes Y, B, H, and K are eligible for Economy to Business Class Upgrade Awards up to 10 days prior to departure.
-CX & KA flights in fare classes J, C, D, and I are eligible for Business Class to First Class Upgrade Awards up to 10 days prior to departure.

AY - Cannot upgrade Codeshares.

IB - Cannot upgrade Codeshares.

JL - Using JAL Mileage Bank:
-Tickets with booking classes J/C/D/Y/B/H/K/L/W printed in the CLASS column of tickets are upgradable.

LA - Cannot upgrade Codeshares.

MA - Cannot upgrade Codeshares

QF - Cannot upgrade Codeshares.

RJ - Using Royal Plus Miles:
-Upgrade is only on Tickets with booking Classes Y , H , K , M, and B.
-Upgrades are not available on Iraqi Destinations.

[B]Disclaimer: I do not have any personal experience with upgrading codeshares as outlined above. I have simply tried to collect data and will have to rely upon other people's firsthand experiences.