If you want an additional bank card for flexibility in spending, then it makes sense.
However, with three bank cards, you are unlikely to improve mix of credti by addition of a fourth.
The primary factor I would consider before applying for a new bank card or seeking CLIs is the liklihood of approval.
What is your current score?
If score is iffy, then I would first concentrate on score improvement. Is the judgment paid? If not, that alone could result in denail, regardless of score.
Keeping % util on existing cards low will give the same current score improvement in util of credit without need for higher CLs or an additional CL on a new card.
Once you are confident that your score and any manual review of derogs in your CR are likely to obtain approval, that is when I would seek more credit.
Personally, I would seek higher CLs rather than an additional card.
