I have personal experience in a situation where a cross-airline-partner connection on separate tickets went awry. I was booked SEA-ORD on an AS ticket, and then ORD-AMS-IST on a separate KL 074 ticket. The AS flight was delayed, causing me to not be able to join the ORD-AMS flight on KL.
AS coordinated with DL staff in SEA, and a compromise was reached - DL took control of my ticket and allowed me to rebook onto SEA-AMS-IST. I had to pay the additional fare collection for the SEA-AMS-IST itinerary on the order of $750/person, but Delta waived the change fees and allowed me to book a V fare (even though it was day of departure), making the additional collection painful but not disastrous.
That was a miserable day of travel and I wouldn't recommend it to anyone, but I did find there was some level of agent discretion (at least regarding waived change fees) even though they weren't obligated to accommodate me. To be fair, though, at the time the DL/AS/KL relationship was a stronger one... I'd expect less generosity in an EK situation.