In my opinion, the answer is a firm No for several reasons.
It seems like you're discussing CSS, but it's not clear if you're referring to the CSS of Bootstrap or the JavaScript of Bootstrap, or possibly both.
Both Bootstrap 3 and 4 have similar styles and JS functions with the same names, which could potentially create conflicts or result in one overwriting the other (usually the last thing loaded takes precedence).
Furthermore, it's important to ensure unity within the team.
It's essential to agree on which version of Bootstrap to use rather than moving in different directions. Having a discussion about the advantages and disadvantages of each version is crucial. While there may be valid reasons for sticking to Bootstrap 3, just because Bootstrap 4 is the latest doesn't mean it has to be automatically adopted. There are numerous examples and best practices available for Bootstrap 3 at this current point in time.
Overall, I recommend focusing on finding solutions to the present issue at hand.