Check out the FAQ on multiple applications at https://workandincome.govt.nz/products/a-z-benefits/employer-questions-and-answers.html#null.

A question and answer applicable to your situation pasted below:

I work multiple part-time jobs. Can I get wage subsidy from all of my different employers?

Yes. As an employee who is employed by two or more different businesses, you can receive the wage subsidy from multiple employers, as long as you meet the usual criteria. We cannot pay the same employer more than once for the same employee, and the wage subsidy rate should reflect whether you’re employed part-time or full-time by that employer.