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They don't mean the same thing at all.
The adverbs '더' and '더욱' are synonymous meaning:
정도나 수준 따위가 한층 심하거나 높게. (Literally) More or higher in degree or level.
They all can be translated to 'more' in English.
However, '더욱이' has a different meaning:
그러한 데다가 더. (Literally) In addition to what has been mentioned.
You can't use '더욱이' in place of '더' and '더욱'.
As @krim mentioned, '더더욱' and '더욱더' are used to emphasize '더욱' and they mean:
‘더욱’을 강조하여 이르는 말. A word emphasizing '더욱'.
The word '더욱더욱' could be different from 더, 더욱, 더더욱, 더욱더 as its focus is on progress.
Which one to use will depend on what you try to mean.