I doubt that it is common. It may even be impossible in many cases. If the postdoc is considered full-time employment then there may be contractual restrictions on other employment.
It might be somewhat common for companies to fund a short visit and pick up expenses for the visit, however.
It is probably also somewhat common that a postdoc will work in a joint arrangement between a university and a company, perhaps because the company provides full or partial funding for the position. But it would still be "one job" and not two. Perhaps that is what you meant by the question, of course.
Doctoral students, in the US, at least, are different than post docs since they are not considered full time employees. They may hold part time (TA, RA) positions, of course.
And, depending on the nature of the position, it might be possible to accept short term employment when the normally expected activities are suspended, such as between terms for example.