Can a legal consulting company collect money privately?

I can't.

Legal consulting companies can only provide legal services to the parties and act as legal advisers, and have no right to collect money privately.

If you want to effectively collect money, you can bring a lawsuit to the court or apply for arbitration.

Creditor's rights certificates such as IOUs, receipts, IOUs and other evidence that can prove the existence of the legal relationship between lending and borrowing shall be submitted to the court.