The existence of water on Mars has been the focus of intense

I do not think the use of in addition to or besides is a real split here. After all, both are synonymous and interchangeable. Secondly, in structure, all the five choices are modifiers, legally modifying the planet. Hence, there is no issue about modification.

The issue whether it should be in both the locations or in any one of them is of little relevance since the focus of the text is to probe whether water ever exists on the planet at ll.

Therefore, the problem lies in the idiomatic description of the modifier itself.

There are five distinct choices for us to tackle now.
1. the possible holding of – the possible holding is unidiomatic
2. the possibility to hold – unidiomatic
3. the possibility that it holds – I can’t find anything wrong with this noun + noun modifier
4. possibly holding – This is also good enough.
5. beside possibly holding – beside is wrong diction in the context.

I would think that the problem with this question is that they are two correct expressions as in both C and D unless one would stand to say that D is preferable because it is less wordy. Anyway skating on very thin ice.