If I file with government & private companies can I collect from both?

A word of warning. If you apply and win a disability judgment from both your employment insurance and Social Security, you will not be collecting double. The two work together to try to make up a portion of your former salary if it is determined that you are unable to work. Sometimes people who were paid the entire sum through their employer and then later were awarded the SSA claim had to refund the difference to the original grantor of benefits.