The petitioning employer files and ordinarily pays the government filing fees, with amounts published in the USCIS fee schedule. What is worth negotiating separately is relocation, housing, tax preparation in two countries, and legal representation for the family's dependant filings.
The visible cost is small; the negotiable cost is everything around it
Employees moving on assignment often assume that because the company files the petition, the company handles everything. In practice the petition is the narrow part. Cross-border tax preparation for the first two years, a household move, a vehicle, temporary accommodation, and a spouse's job search all have costs, and none of them are immigration fees. Assignment terms should be written down: what is reimbursed, for how long, and what happens if the assignment is cut short or extended. Ask specifically whether the company's legal counsel also represents the family for dependant filings, because counsel engaged by the employer represents the employer, and a spouse with a complicated history may need their own advice.
Hypothetical example: a turbine-blade coating specialist receives an offer silent on taxes and early return costs. The review should decide which relocation obligations need written agreement, using the assignment package, tax advice, housing terms, and return provisions. Put the payer, payment date, and refund condition beside every item before money moves. Check current government figures directly. The recurring error is that a covered petition fee is not a complete household relocation agreement. Financial planning follows the substantive eligibility analysis.
Put exclusions in writing before the household incurs them.