I just finished the rendering. I am not satisfied with the final result. I want to push it further. Is there a way to increase the rendering sample to continue rendering based on this result without starting over again?
It depends on how you rendered the image. During rendering samples are simply averaged, but if you use denoising then AI processes the image. If you rendered an image without denoising with one seed and restarted the render with another seed, you would get different samples so you could just average the two images depending on amount of samples and it would be the same result as if you just continued rendering. They can be simply mixed. It would be ideal to render to lossless EXR format.
If you have a look, the mix is less noisy than the parts on their own.
The images were rendered with different seeds. Seed number can be changed in Render Properties tab, Sampling panel, Advanced sub-panel:
This should work with simple 8 bit per channel images as well and the image should improve even if denoising was used, but it might not be exactly the same as just continuing the render. There will probably be some detail loss if you mix images with denoising. Only if you save renders to EXR, you get raw data from render, not altered, compressed or clipped by color management so you can only get exactly same results as if you continue rendering with EXRs.