Inheritance chain vs multiple extensions

Is inheritance chaining something that should be avoided?

I'm currently in the process of refactoring a java project and I have come across a number of classes (8) which all of them have a shared functionality. So, using the Extract Super Class refactoring, I created a super class with that functionality and passed it to all the sub-classes. Now, 2 of the classes have also a second shared functionality. Should I create another super class which inherits from the first super class and, in turn, is extended by the sub-classes or simply extend multiple classes on the 2 sub-classes?

Thoughts

Even though both options would work, I feel that going for multiple extensions is preferable since it describes and clarifies the responsibilities of the class. Also, we would avoid making continuous super() calls in order to reach the top super class.
On the other hand, maybe having an inheritance chain kinda tidies up the place.