Sometimes, I often particularly enjoy puzzles that reuse the same piece of information over and over. Essentially, it shares the elegance of a well constructed &lit, with whole text serving double-duty. Every word not only is used in entirety for the wordplay part, but the whole phrase could serve as a plausible definition too! Some more examples to follow:
Encoding several different messages in the same piece of text, each one leading to the next by instructions.
Extraction from the same ciphertext twice, using (ideally) two different ciphers - could be overambitious, but this theme is ambitious.
Next, a picture that has three interpretations - although, this is close to puzzle sets, so try to seamlessly integrate the pieces.
Letters arranged in a grid. Extraction can appear in multiple ways - for example, some letters could be a word search, others from a grille.
Note that simply reducing information and applying a recursive step isn't necessarily this - that would be using newly acquired data. Going back to square one is this theme's spirit! Then start over, with a fresh look, either by sheer inspiration or by explicit instruction. Have you noticed that this suggestion is itself a puzzle that self-illustrates this theme?