Can I keep my Working KITAS when I change my job?

Unfortunately, no.
A Working KITAS is tied to your employer, not to you personally.
If you change your job, your current KITAS becomes invalid.

You must:

1. Obtain an EPO (Exit Permit Only) to close your existing KITAS, and then

2. Your new employer must apply for a new Work KITAS on your behalf.

Without following this process, you cannot legally work for a different company in Indonesia.