[RPG] Can you Multiattack twice with the Extra Attack Feature

If you have the ability to make multiple attacks in a round, they can be against the same target or another target unless the specific ability prohibits it.

You can move between attacks, as mentioned on page 190 of the PHB.

Moving between Attacks

If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks.

No, even monsters only get one action per turn, and actions should not be confused with attacks. in the case of monsters that can attack multiple times, that's because Multiattack is one action, that just happens to result in attacking more than once. Each attack is not an attack action! Multiattack is also very specific about which attacks the action results in.

So an owlbear can indeed grapple or shove, but that grapple or shove is done by taking a normal Attack action, not a Multiattack action. The Attack action is general purpose and more flexible than Multiattack, but doesn't allow the owlbear to make more than one attack during the action.