Bismillāh al-Raḥmān al-Raḥīm
Thank you for your question. As long as there is no stipulation in the marriage contract to the contrary a man is entitled to up to four permanent wives in Islamic law and that is not contingent on the approval of any of his wives.
It is of course wise to seek approval from any current wives, but that is not a condition for the validity of another marriage contract and not having the approval of a previous wife would not mean that the following marriage was sinful in any way.
May you always be successful.