Variant (1) is hardly new. Look for (Balanced) Marseillais Chess. (e.g. https://www.chessvariants.com/multimove.dir/marseill.html )
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1. Twofold Chess
White plays first opening move.
Both players are then allowed two turns thereafter.
It would seem easy enough to code for this and could open up some highly entertaining new strategies.
2. Chess Refuge
Whenever a player is placed in check, they then are allowed an extra second turn to escape and possibly even counterattack.
If checkmate though, gameplay is over.
Any thoughts on these two concepts?
What might be the best way for these to ever become a reality?
Cheers.