Can I Quicken a cantrip to cast it twice in a turn and also use Twinned Spell on both castings?

I’m currently building a monk sorcerer who uses melee spell attacks, notably the cantrip Shocking Grasp. Can I use the Quickened Spell Metamagic option to cast the spell as a bonus action and then use the Twinned Spell Metamagic option to attack an additional enemy, then use Shocking Grasp again as my action and use Twinned Spell again to attack both enemies a second time?