In my experience, unless you have a VERY narrow field of application you aren't going to be effective with just the knowledge imparted by one branch of engineering. For example: most of my career has been spent designing, manufacturing, testing, and troubleshooting rotating electrical machines. By default, that requires a knowledge of electrical engineering - particularly the physics of electricity and magnetism, as well as both linear and rotational motion. That being said, a lot of the "extra" background got its start in the early semesters of my chosen program (because it is assumed that the students don't really know what they want, so are exposed to all engineering tracks plus some other courses), with considerable additional learning after I was actually out in the workforce.
Within the electrical field alone, it requires knowledge of some specific subsets: magnetics and machine design, power transmission and distribution, power electronics, VLSI (Very Large-Scale Integration, which basically means designing computer chips), antennas, and radio-frequency applications.
However, it ALSO requires significant knowledge in chemistry (for insulations and material properties), mechanical engineering (for material properties, torque transmission, foundation design, structural integrity, and both static and dynamic performance), civil engineering (foundation design and transportation capabilities), process and industrial engineering (how things are supposed to work and what the end objective is), finance (how to pay for materials and the finished equipment), fluency in at least one written language (to effectively communicate ideas to others), mathematics (to figure out how to perform all the necessary calculations to translate an idea from words to actual motion and equipment), and interpersonal skills (how to deal with people).
In some specific instances, it also requires at least some knowledge of medicine (think prosthetics) and various environmental effects (think land-based systems vs offshore locations vs air or space).