thanks for the interesting question, you need to consider first the preparation method of your support, which affect the final prepared catalyst. Alumina can be used as an active catalyst as it showed acidic sites (mainly Lewis acidic sites) and also it can be used as a support and this is due to its high surface area, mechanically stable and the porous structure.
For instance, different precursor and calcination temperatures can lead to different types of alumina support in term of acidity, surface area, activity....etc. Please find the attached paper that discussed the different phases of alumina and the effect of the precursor, calcination temperature on the prepared alumina catalyst