Attorneys postponed a preliminary hearing on Monday for Ger Lee, Billy Xiong, Anthony Montes and Porge Kue.
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Prosecutors are now scheduled to present the first evidence in the case in August.
The men are accused of being gang members who opened fire at the party in November 2019, killing four people and injuring six others.
They were allegedly retaliating for another murder earlier the same day but allegedly hit random targets instead of rival gang members.