Can small businesses work with these big construction companies?

Yes, it is common in that biggest construction firms will be having some contacts with small businesses in terms of subcontracting. They also find it difficult to do specialized works such as plumbing, electricity, landscaping or concrete work on large projects. Big companies are also required by government projects to involve small, local, or minority owned businesses in their contracts. This presents small companies with a chance to expand by collaborating with such giants in the field as Bechtel or Kiewit