I could be proven wrong, but the precedent at this point says that Kate/Sophie is far less likely to happen - especially with Sophie not being "out" - than people seem to be assuming.
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"Oh, brilliant" - Thirteenth Doctor
"Half an hour ago I was a white-haired scotsman." - Thirteenth Doctor
"I know exactly who I am. I’m The Doctor." - Thirteenth Doctor
"Two hearts. One happy. One sad." - Thirteenth Doctor
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