There is no limit on the profit a company may take, though on Cost-Plus contracts the government may explicitly state the profit margin a company is allowed based upon performance metrics. The government CAN, however, audit your books for DCAA compliance on T&M (time and materials) and Cost-Plus contracts to ensure what's being charged to them isn't overly inflated.
On fixed-price contracts, however, companies can pull in 20-25% net margins sometimes. The average net margin on all contracts is between 8% and 12%. You can verify this by looking at the financials of the publicly traded contracting firms like Booz Allen and Leidos who are all in that 8% to 12% net margin range. There is no limit on these margins set by the government, however, just guidelines on what is "acceptable" to them to be included in your pricing (costs and profits passed on in the form of billed fully-loaded labor rates for hourly work).
It's actually more profitable for companies to do contractor-facilities (remote) work on a fixed-price basis, contrary to what people outside of the industry think.