On maximizing curves of degree $7$

In the present paper we investigate the question concerning the existence of maximizing curves of degree $7$ with some prescribed $\mathrm{A}\mathrm{D}\mathrm{E}$ singularities. We give a result proving the non-existence of such maximizing septics and we provide new examples of conic-line arrangements with some $\mathrm{A}\mathrm{D}\mathrm{E}$ singularities that are free but not maximizing.