When the 副助詞（ふくじょし） (adverbial particle) でも is used more than once in a sequence, it is an extension of one of its regular meanings, 類推（るいすい） ‘analogical reasoning’. However, several ‘analogies’ are being presented.
This use of でも is regularly translated as ‘whether it is (A), or (B)’, or ‘neither (A) nor (B)’, depending on whether the rest of the phrase is positive, or negative.

• サッカーでもバスケットボールでもいいからスポーツをやりたい。
  Regardless of whether it is soccer or basketball, I want to play sports.
• ケーキでもクッキーでも苺（いちご）が入（はい）っていたらどちらも食（た）べない。
  Even if it is a cake or a cookie, I will not eat it if it has strawberries in it.

Literally, the translation of 〜でも〜でも is closer to the following:
Even if it’s (A), even if it’s (B), (C) is the result. (In a positive sentence)
Even if it’s (A), even if it’s (B), (C) is not the result. (In a negative sentence)