I'm doing exactly this. Making a consistent income from a fairly hands-off fintech startup, but wanted to leverage my time so am working full-time in a related area.
Made full disclosure on all my interests and activities with my employers before I joined a couple of months ago. To my surprise they didn't see a problem. It's understood I cannot take part in anything that might lead to a conflict of interest.
Long story short: it can work fine with good will on both sides. But do be completely open about what you are doing. I got a statement, in writing, that my outside interests would not cause a problem and suggest you do too.
Made full disclosure on all my interests and activities with my employers before I joined a couple of months ago. To my surprise they didn't see a problem. It's understood I cannot take part in anything that might lead to a conflict of interest.
Long story short: it can work fine with good will on both sides. But do be completely open about what you are doing. I got a statement, in writing, that my outside interests would not cause a problem and suggest you do too.