1. Doesn't matter if you're in the business of widgets or SaaS or whatever. Business is business.
2. There are really only two engineering disciplines you need a strong intuitive understanding of: systems and physics.
It is completely possible to be very skillful at all three of these. However, even for Elon Musk, it would still likely take months of training to keep up working in a new engineering discipline including all of the idiosyncrasies and tools. There are plenty of people who are highly knowledgeable in 5+ subjects, but virtually none who are capable of working as a diverse, skilled experts in more than 3.
If you want to be an expert in multiple fields, find underlying 'core' disciplines and become an expert on those.
To start one is problem solving, you need to be really good at solving problems. Another I can think of is finding the right problems to solve.
Most people can't do it. Recipes are required. Do that to obtain X result. And most people apply known principles and methods in order to obtain what they want. But if you understand how it all fits together, you create your own recipes. This is what we call innovation.
Some people manage to do it through brute force. Some people are simply born different. And it all boils down to what you want from life. There is no easy answer. Some people are simply driven and also have the mental capacity to understand.