iTunes Store, App Store experience partial outage

Several users are reporting this morning that both the iTunes Store and App Store are down. In many cases, the stores will give "cannot complete your request" messages, or simply fail to download purchased items.
Apple has not yet updated its System Status page to reflect any issue. It should be noted that this seems to be only a partial outage, as many are still able to access both stores and download content from them.
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Joseph Keller is the former Editor in Chief of iMore. An Apple user for almost 20 years, he spends his time learning the ins and outs of iOS and macOS, always finding ways of getting the most out of his iPhone, iPad, Apple Watch, and Mac.