How to implement multiple intersection and union clippings

I am developing an SVG converter for a specific purpose. SVG version is 1.1 which is a bit old, but I have to use this version.

I'm having a hard time trying to implement a clip list.

The clip structure is as follows.

struct
{
    edgeList *path
    clip *intersect
    clip *union    
} clip

Any clip object can have a intersecting clip or union clip or neither (but not both). So if there is an intersecting clip, I have to use intersect that clip path with the parent. If there is a union clip, I have to combine it with the parent.

According to SVG specification, I can use intersection of two clips by defining the two clipPath elements and using one of them in the clip-path attribute of the other clipPath. Union can be implemented such that you define both paths inside on clipPath element.

Now, what if I get a multiple clip paths? Say for example, 5 of them such that,

1. The first two clips should intersect with each other
2. The 3rd clip should combine with the previous result
3. The 4th clip should intersect with the previous result
4. The 5th clip should combine with the previous result

Note: The combined black area is the final clip area.

I can try to implement it like this.

<defs>
<clipPath id=cp1>
    <path>red</path>
<clipPath>
<clipPath id=cp2 clip-path="#cp3">
    <path clip-path="#cp1">green</path>
    <path>purple</path>    
<clipPath>
<clipPath id=cp3>
    <path>yellow</path>
<clipPath>
</defs>

And I'm stuck at the 5th clip.

How would I union this? Besides, this method is harder to do programmatically. Is there a better way this? If there is no other way, I guess I will have to put it off as a limitation of SVG.