After the CMC, a new micelle is formed. The micelle can have a limited number of molecules. Therefore, as the concentration is increased incoming new molecules form another micelle.

Above the cmc, micellar structures will form. As the amount of surfactant increases, these structures may no longer be the traditional spherical micelles most people consider. Describing it simply, the first are rod-shaped. At higher concentrations, lamellar micelles may form which are liquid crystals. Other shapes may also form.

A more thorough description can be seen in Figure 3 of this paper:

https://www.mdpi.com/2079-4991/7/10/305

Above the cmc, even before non-spherical or liquid crystal structures appear, the number of micelles increases and, consequently, almost linearly, the solubilizing power of the medium, especially towards hydrophobic solutes. On the other hand, surface tension does not change much.

The cmc is the highest concentration of free detergent molecules possible in a solution. If the total detergent concentration is higher than the cmc, the excess goes into micelles.

For solubilisation, free detergent molecules partition into the phospholipid membrane, until you have a concentrated solution of detergent in lipid. Then, solubilisation occurs, forming lipid/detergent/protein mixed micelles. For membrane protein purification, you want a maximum of one protein molecule per micelle (otherwise you can't separate them); because of Poisson-statistics that means that you need about 10 micelles per protein molecule. See doi:10.1590/S0100-879X2002000700001 for a review.

The cmc is the highest concentration of free detergent molecules possible in a solution. If the total detergent concentration is higher than the cmc, the excess goes into micelles.

For solubilisation, free detergent molecules partition into the phospholipid membrane, until you have a concentrated solution of detergent in lipid. Then, solubilisation occurs, forming lipid/detergent/protein mixed micelles. For membrane protein purification, you want a maximum of one protein molecule per micelle (otherwise you can't separate them); because of Poisson-statistics that means that you need about 10 micelles per protein molecule. See doi:10.1590/S0100-879X2002000700001 for a review.

thank you Engelbert Buxbaum