We investigate the additivity A and lineability L cardinal coefficients for the following classes of functions:
ES \ SES of everywhere surjective functions that are not strongly everywhere surjective,
Darboux-like, Sierpinski-Zygmund, surjective, and their corresponding intersections.
The classes SES and ES have been shown to be 2^{c}-lineable.
In contrast, although we prove here that ES \ SES$ is c^{+}-lineable,
it is still unclear whether it can be proved in ZFC that ES \ SES is 2^{c}-lineable.
Moreover, we prove that if c is a regular cardinal number, then A(ES \ SES)≤ c.
This shows that, for the class ES \ SES, there is an unusual big gap between the numbers A and L.

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**Last modified December 20, 2016.**