MR=MC rule's application

I am struggling with some economics concepts -

On one hand, we learned that different markets (perfect competition, oligopoly, etc.) share the same rule - profit will be maximized when MR=MC. Take monopoly market for example, to maximize profit, monopolists will expand output until MR equals MC.

On another hand, monopolist using the price discrimination strategy can achieve smaller deadweight loss and bigger profit, compared with monopolist without price discrimination strategy (even though the latter one already makes sure MR=MC).

So my questions are… take the above-mentioned case for example, does it mean that producing “optimal output Q” when MR=MC actually cannot guarantee monopolist with maximized profit? If so, how shall we look at the universal “MR=MC” rule’s application to various markets?

Thanks in advance for your clarification.

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The idea behind MC = MR is to establish the output quantity that maximizes profit. If you have no price discrimination, you will maximize your profit when MC = MR. If you have price discrimination, you will also maximize your profit when MC = MR (and that maximum profit will be bigger than the maximum profit with no price discrimination).

Yeah the idea behind MC = MR is to establish the output quantity that maximizes profit, and then selling price is determined from the price on the demand curve.

Are you suggesting that with price discrimination, the MR curve will be different (compared with the MR curve without price discrimination)? Thus using the same rule MC=MR, we will get a different Q and better profit accordingly?