It is possible to mix eggshell and semi gloss paints together with some careful preparation. For best results, you should choose one sheen and stick with it for the whole project. But if for some reason or another you have two different sheens of paint to use and they are the same color and same brand, mixing them together is an adequate solution.
Both paints must be latex. Do not mix oil-based with latex-based paints; this would work as well as mixing oil with water.
To get the best results, use the same brand and line of paints. Don't mix Benjamin Moore with Sherwin Williams, but instead mix Sherwin Williams with Sherwin Williams.
Furthermore, it is best if the same line within the paint brand is used. For instance, rather than mixing Sherwin Williams Duration with Sherwin Williams Cashmere, use one or the other. If you mix different brands or even different lines within the same brand, there can be compatibility problems that will cause a nonuniform look.
Put both paints in a separate, clean container and mix using a stir stick or drill with a mixer.
Mix the paints well. If you fail to mix completely, the result can be streaking or different sheens in different parts of the room.
While painting, it is important to shake the container or mix the paint each time before pouring into a trim pail or roller tray for application.
Each sheen and type of paint is formulated with a specific purpose in mind, so don't expect to get the same quality when mixing.
Do not mix interior and exterior paints.
Have enough paint to do the whole project because it isn't possible for a paint store to match a custom-made sheen.