The closest Heinlein story I can think of off the top of my head is "We Also Walk Dogs." It doesn't quiiiite fit though.
In the story, General Services has an international reputation that they handle any and every job no matter how big or how small. The title of the story is the company motto, acknowledging that they started as a dog-walking business and still offer those services.
As memory serves, Earth finds itself hosting an intergalactic UN but doesn't have the technology to keep all the delegates in their specific habitats, let alone the incredible organization required. Desperate, they turn to the Corporation and dump the problem in their laps with an unlimited budget.
The corporation handles it like a whirling dervish, finding scientists who had been researching gravity manipulation (for delegates who had high/low gravity needs) but whose funding was cut, and stick them in cutting edge labs with all the resources they could want, and various other things.
They manage to pull everything off in time, but in doing so they pull humanity technologically up by the bootstraps, opening a new way for the future, with them positioned having the patents for every single technological advance and ready and willing and able to be the faithful (and well compensated) companion and guide that humanity needs to usher it into its future.