Supplementary self-employment for non-EU workers in the EU

In which European countries can a non-EU citizen do supplementary self-employment in addition to keep working in his main job and without having to change his visa type?

I am a Syrian graphic designer and I want to start looking for jobs in the EU. In addition to this, I would really like to be able to sell digital prints online on Etsy (for example) to help support my living costs and my family at home. This additional thing will roughly take me one hour each day so it won't affect my main work.

As far as I understand, in some countries you can't do self-employment and be employed at the same time. Are there any EU countries that allow this for non-EU residents?

Thank you, I appreciate any answers ^_^

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