Multiple residence permit

I am a non-EU person with researcher residence permit in Italy. While, my wife had a Blue card in Germany. Though, I can travel to Germany on my residence permit however, I want to apply residence permit in Germany for myself and a residence permit of Italy for my wife.

Questions

• As far as I understood, I can have multiple residence permit, can
  some one confirm this?
• Give this scenario, can someone suggest a
  better option?