This is a great suggestion - many of the big name consulting companies (Accenture, Ernst & Young, McKinsey, CGI, Capco) will happily subcontract out the work that they've sold, or bring on external consultants to fill out a team.
Any advice on how to find the right person to talk to at these firms? I used to work at Deloitte, and even there I haven't figured out how to sub on something.
I can connect you to the right person at Accenture at least, email me kthejoker gmail