Does Temtem have cross-play and cross-progression?

While Temtem initially launched in 2020, developed by Crema and published by Humble Bundle, it arrived later on PlayStation 5, Nintendo Switch, and Xbox Series X|S consoles.

Switch, PS5, XBX] Temtem $36 (RRP $79.95) + Delivery ($0 with Prime/ $39 Spend) @ AU - OzBargain

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Does Temtem have cross-play and cross-progression?

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