If the Parallel City Stadium is already in play, can either player replace it with another Parallel City card facing the opposite direction?
No. Stadium cards can only be replaced by another Stadium card with a different name; direction of the card does not matter.
Source: BREAKthrough FAQ (2015-11-19), TPCi Rules Team (2015-11-19)

Relevant cards

Note: All applicable cards may not be listed below.
XY8_145