Hello,
For documentation purposes, I will post a workaround I have applied to this problem, which I found to be practicable enough for me, even though is not as automatic as I would like a BIM software to be.
Consider the structure below and imagine we have a floor plan which typically matches with the top face of the beam. We would like the floor plan to apply a different filling Pattern to the columns A, B and C, since column A continues to the next floor, column B starts on this floor, and column C ends on this floor, considering the typical direction of structure execution.

So, first of all it is necessary to divide the columns in Parts (Modify > Create > Create Parts), utilizing the floor levels as references for the division. Since I am working with Reinforced Concrete, this makes sense as each level will be executed in different phases and, although all the levels are part of a single column in the project, a column is executed, and sometimes designed, in parts, which aligns with this concept.
Ok, so the next step is defining complementary patterns for Parts and Structural Columns in the Visibility/Graphic Overrides panel, in the Properties tab for the floor plan view you are at. The "complementary" part will be evident further in the result below, but it basically means that the Cut Pattern for Parts should not be "overwritten" by the Cut Pattern for Structural Columns, and vice-versa. For example:

As you can see, the hatch for both Cut Pattern Parts and Structural Columns have different directions regarding each other, being visible if overlapped.
The last part is defining the View Range, most specifically the Cut Plane, which should cut above the floor plan level. A value of 30 cm is what I used here, but you can change that to any value that would cut above the floor plan, and below the next one. In this way, all the columns (A, B, C) are visible. Also, in the Properties panel, you should set the Parts Visibility parameter to Show Both, so the plan view shows both Parts and Original elements.
As you can notice, with this configuration, the column C will not be cut, as expected, and will show a pattern related to the Projection/Surface Pattern. The columns A and B will show the Cut Pattern for both Parts and Structural Columns, as indicated on the previous image. Here is the part where the workaround occurs, which is a manual configuration: you should select the Part instance of column B and, with a right-click of the mouse, select Hide in View > Element. This way the related hatch will disappear and you will have a different pattern for each column, as illustrated below.

It is not a manual workaround, and therefore it is very susceptible to human error, but at least you just have to apply this to the column that is starting on the given floor each time. Also, I have concluded it should not be possible to find a automatic solution to this within the actual Revit, since it only lets you apply to the same object just two different patterns, and I cant imagine any solution to obtaining three different patterns without using another object, such as Parts.
Last, this is definitely a question for the Revit Structure forum, but since it related to graphical representation I thought someone here could know how to solve it. I tried to post a question on the Revit Structure forum, but just now I have found that I forgot to upload it there. I will see if someone over there has a better solution and will post the link here.