Jelly, 4 bytes

R»µ¡

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R»µ¡
R     Range. 2 -> [1, 2]
 »    Max between left arg and right arg. Vectorizes. -> [2, 2]
  µ   Separates into a new chain.
   ¡  Repeat 2 times. After another iteration this yields [[2, 2], [2, 2]].

Jelly, 4 bytes

R»µ¡

Try it online!

R»µ¡
R     Range. 2 -> [1, 2]
 »    Max between left arg and right arg. Vectorizes. -> [2, 2]
  µ   Separates into a new chain.
   ¡  Repeat 2 times. After another iteration this yields [[2, 2], [2, 2]].

Same thing but with a single monad and no need for the chain separator:

4 bytes

»€`¡