To initiate a Virtual Party Show, it's imperative that the Temptation intending to start the event has added you to their Friend List. You can read more here.
When another Temptation begins a Live Show, you can express your interest in participating by utilizing the Send a Request button in the chat box located at the bottom right of the screen. Upon the other Temptation accepting your request, the Virtual Party Show commences. It's important to bear in mind that the decision to accept or reject your request lies with the other Temptation. They have the discretion to choose whether to include you in the Virtual Party Show or decline your participation.