Your character can do things not covered by the actions in this chapter […] The only limits to the actions you can attempt are your imagination and your character's ability scores. (PHB, p. 193)

Melee isn't limited to or defined by a list of mechanical actions. Creative maneuvers in combat are not only possible, they're expected by the game and it provides rules for them. Flip to page 193 and read the sidebar — it's a core rule, notice, not marked as a variant or optional rule.

To reposition an enemy by flipping them, you just need your DM's buy-in that it's possible or reasonable (because ruling on that sort of thing is the DM's job), and then they and you will use the Improvising an Action rule to resolve it. It's a simple process:

1. Describe what you're attempting
2. The DM decides if it's possible
3. If so, they tell you what to roll

When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.

The rules for Multiattack in the Monster Manual (page 11) are perfectly clear:

A creature that can make multiple attacks on its turn has the Multiattack ability. A creature can’t use Multiattack when making an opportunity attack, which must be a single melee attack.

Or, in other words, it works exactly the same way as Extra Attack, and can't be used with the Ready action.