Unfortunately, stains are not compatible other than the base thinner. Companies do each color differently, so there will be differences in the final shade.

You might be able to get close, but the result may not be something you like.

Matching the colors between two different company's product is possible, but it would take many attempts and lots of different colors to do so.

There are two possible ways to get a good result, however. As always, testing is necessary.

One, get close with another brand and then use a darker color for the final color. For example, using the color chart linked:Minwax color chart

Original stain Golden Oak. Finish the dresser in Minwax Golden oak and if the colors do not match, use Early American as the final color.

The other option is to use a gel stain. Gel stains are more paint than stain. I have never used a gel stain, so am making this option based solely on what I read. You would still need to finish the first application to even out the base color.