are making can go ahead without continuing support for the previous version - then you know whether it is UC or NUC. If it is NUC, then you need to first identify if there's an UC (sounds the same as "a NUC!") way of doing the same thing. You'll be surprised at the ingenuity when someone understands the impact of their change.
NUC to UC Transformation
If you cannot find an UC way, then you need to break it down into a series of steps that make the "NUCness" easier to swallow. First identify all of the customer (in the broader sense) affecting elements and how they affect each customer. Then identify the best way to prepare the customer to accept the change most easliy. Maybe it's adding a data field to the schema ahead of time. Maybe it's retro-fitting a feature into the current customer release first. Maybe it's throwing a party for them on the day the system is going to be out of service! You want to isolate the incompatibility from the rest of the change as much as possible, and make it less visible to the customer.
Don't bundle UC changes with the NUC changes where you can avoid it. Your job is basically to identify a way to transform the NUC change into an UC one, with as little risk and impact as possible. OK, our network is going to be down for 2 hours. If all the NUC stuff, and only the NUC stuff is done in that 2 hours, it's easier to believe the downtime estimate. It's easier to roll back if something goes wrong. It's easier to understand the risks. Then when the network is back up, add the rest of the changes in - the same day or over the next few weeks. Unless there's an urgent concern, it won't matter much. And the customer knows the network will remain up.
Eventually you'll start to use foresight, like enabling the previous release, before it is shipped, with the proper data structures so that conversion to the next release is painless. If you work at identifying (and I would argue implementing) NUC changes near the beginning of your release development cycle, there's a good chance you'll have time to put some hooks into the previous release before it's widely distributed.