Moderation and Mediation in one analysis?

Hey everyone I'm new here and I hope that I'm in the correct forum and someone can help me :)

I actually feel like I have a very basic question but I am quite new to statistical analysis and would be grateful for any help!

I am writing a research paper for class and chose my own research question and hypotheses.
I am a little confused method-wise, because I fell like doing a moderation and a mediation analysis (with different moderators/mediators) would make sense to answer my research question, so my question would be if it's allowed/common in a research paper to work with two different methods to answer the research question?

Thanks in advance :)
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Less is more. Stay pure. Stay poor.
People do use such approaches but they have background knowledge to justify their use. So they can justify the possibility of a mediated moderator or moderated mediator. Just trying to see if they exist in a dataset without justification runs the risk of false discovery. Side comment, just to introduce a moderator (variable of interest's effect differs on outcome within the categories of another variable) requires a lot more data to conclusive examine it. Now add a mediator on top of that - you will require even more data than if you were just going to do an analysis without them. This is given you are comparing effects within subgroups now. Lastly, say either the moderator or mediator was binary, well it is likely not going to be balanced (half the people in each group). This imbalance is going to require even more data to power its examination.