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Have any researches compared reading many texts at the same level vs reading one text at different levels?
Would it be effective to read the same book or any text repeatedly, but at different level (grade) each time?
For example, British council site has many texts at 3 levels (A1, A2, B1, B2) with separate exercises for each level. (Level 1 text and Level 2 text)
Is it better for learners to read only what suits their current level or to practice all 3 texts with exercises for more exposure?
Low level texts are designed to be readable for beginners. For example, B1-level texts are supposed to contain words, which are expected to be known on this level and which has chance to be a part in text in B1-exam.
Reading texts of higher level helps you to broaden your passive vocabulary. It's great idea to read a book you know in a different level (or origin). Reading stays interesting (because you know what's going on) and helpful (concerning broadening your vocabulary).
First of all I think your terminology for B1 or C2 text level is not widely used.
Simplified text is called graded reader. There are a lot of publishers who prepares graded text.
CERF doesn't define grammar and word count for each level.
What you presented is a naming schema of concrete publisher and you should stick to recommendation of that publisher. Most respected publishers provides description or teacher books that explain how to use their book series materials.
Word frequency analysis for English texts is a subject of study by prof. Paul Nation since 1970 till today. He has opened access to most of his publication.
I recommend you to get familiar with his writing Hirsh, D. and Nation, I.S.P. (1992) What vocabulary size is needed to read unsimplified texts for pleasure?. Despite it is scientific report it was written as common easy text.
His main point is that common 2000 word level is not sufficient to read unsimplified English text because at this level you see one unknown word on every line of text at average. His analysis shown that 5000-6000 vocabulary is necessary for pleased reading.
One of interesting implication from Paul Nation works is that learning vocabulary from reading become useless after 7000-8000 words because in order to have repetition for some low frequency words you should read at least 4-10 books!
Back to your original question. Learning is about practice and repetition.
Reading easier text to your level provide additional practice/repetition but at cost of spending time that you may spend on other activities. If you feel gaps in easy material - train that material, if not - move further!
Reading hard text violates another rule. You should understand what you try to remember. At very hard level too many words would be unknown and you can't infer word meaning from context. In this case you quickly become bored by looking for word definition in dictionary...
Today technology allow audio form of books. You may spend time on listening what you just read and this provide a new activity instead of boring reading again the same on a different level.
Example of graded text for English with supplementary audio at USA department of States at no cost (in Public Domain).
