With Illustrator, I'd basically use the same technique I posed in this question.
Create base artwork.
Object > Envelope Distort > make with Mesh
Adjust the mesh.
Once you have the mesh, you can move the mesh points, add new ones, etc to create different "blobs".
I started with rectangles but really you can start with any configuration of objects which touch each other - heck, even if they overlap a little it won't matter for the mesh. Using the mesh will keep shapes from overlapping and leading to the "layered' perception. Rectangles, or straight edges which butt against each other help to ensure that no "gaps" are created when moving things around in the mesh though.
It's also possible to use more automated adjusting such as rotating a couple mesh points, scaling mesh points, etc. rather than manually moving everything.
You can also readjust the colors by using
Object > Envelope Edit Contents and merely changing a fill color
Or add more objects.. Drew 2 circles, copied, Edit Mesh contents, select a rectangle, paste in front, then move to front so they are on top of all the rectangles.