Is there any way you can keep on painting on an oil painting using acrylics?
Not start at new painting!
Maybe you can add something to the acrylic paint?
(I know they dont mix well,thats not the question)
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As Catija implied, if your oil painting is less than 6 months old you shouldn’t do this. And if the oil paint is impasto (very thick) you should wait up to 18 months before varnishing. A very bad technique that would work is to varnish with a solvent-based varnish, let cure for 72 hours and then overcoat the varnish with a water-based varnish. Then you could theoretically paint with acrylics on top of this, but if your substrate is canvas I can promise you that you will sooner or later see cracking and flaking - especially if the “final” hanging place has humidity swings.
One last reason why this is not a good approach is that conservators will find it pretty much impossible to restore this kind of work. Basically you are dooming the painting to be more temporary than necessary.
Why don’t you just use oils?
You should never paint over oils with acrylics. The reason for this is that acrylics are essentially a plastic and not breathable. Oils, however, release gases over time. If you paint acrylics on top of oil, the released gases will cause the acrylic paint layer to crack and flake off as the gases try to escape. This result will be amplified in fresher oil paint.
You can, however, paint oil over oil and oil over acrylic.