Add a new Copy Artifact option "Copy from downstream build".
This would only be useful if the job made use of the synchronous (wait to complete) usage of a "Trigger a Build" build step from the Parameterized Trigger Plugin.
When enabled, the plugin could query the downstream job, looking for any job whose UPSTREAM job matched the current job and build number. If one were found, artifacts from that build could be selected.
There would be a weird situation: if a job used MORE THAN ONE "Trigger a Build" in a synchronous fashion, then tried to retrieve artifacts from that build. If the default behavior was to copy artifacts from the MOST RECENT downstream build, that would be fine.