The L.A. school funded by the Bill [1]and Melinda Gates[2] Foundation is about to face new claims of bullying -- including one incident involving a 14-year-old trying to kill herself.

Sources tell TMZ ... there is a new lawsuit about to be filed by the same lawyers at Geragos & Geragos who filed the first suit against the Animo Westside Charter Middle School. As TMZ first showed you ... that initial suit surrounds this video of one student choking another, whose parents claim he suffered permanent brain damage in the incident.

We're told the forthcoming suit documents the alleged bullying experienced by a now-14-year-old girl, who's claiming she too was mercilessly bullied last year on the campus ... and the school failed to stop it.

Our sources say the girl is claiming to have suffered both physical and verbal abuse from multiple students, with one girl leading the pack. We're told it got so bad, the alleged victim started cutting herself ... and months later, attempted suicide.

She had to be hospitalized on a psychiatric hold as a result. Her family is blaming the school as well as Green Dot -- the organization that operates the school.

Bill and Melinda Gates are not being sued, and neither is their foundation ... which has donated more than $7 million to Green Dot.

We're told the girl's family believes there is video of at least some of the bullying incidents she allegedly endured -- and their attorneys are working on getting their hands on it.

Our sources also say since we broke the story about

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