Is it permissible for employees to be paid for completing tasks for investors and contractors that their own staff are unable to perform, provided that they do not neglect their primary duties?

If the employer gives permission, then there is no harm in carrying out work for investors and contractors for a fee during official working hours. Otherwise, it is not permissible, because an employee is a private hire (ajīr khāṣṣ) who must devote himself to the employer, in accordance with the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions." As for carrying out work outside of working hours, there is no harm in requesting payment for it.