To my understanding, in Islam a person doesn’t need permission from the current wife(ves), but the person must inform existing wife(ves) of his intentions for additional marriage.
l think a god fearing and righteous person would give at least a few months of advance notice to his existing wife(ves) and consult with them before taking the next step. This will give wives enough time to think and decide to either stay, leave or negotiate some arrangement with husband. Furthermore, the husband need to have a good reason for additional marriages, not merely for pleasure. I think the main reason Islam allows multiple marriages is to help women in need; otherwise Islam emphasizes on only one marriage.