Lineability, spaceability, and additivity cardinals for Darboux-like functions

We introduce the concept of {\em maximal lineability cardinal number}, $\text{mL}(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\text{HL}(M)$, and lineability $\text{LL}(M)$ of $M$. In particular, we will describe, in terms of $\text{LL}$, the lineability and spaceability of the families of the following Darboux-like functions on ${\mathrm{\Re }}^n$, $n\ge 1$: extendable, Jones, and almost continuous functions.