Posso adicionar primeiro um fragmento a um modo de exibição, depois "desanexar" e "vinculá-lo novamente" a outro modo de exibição?

No código, eu quero:

fragOne one = new fragOne();
getSupportFragmentManager().beginTransaction()
        .add(R.id.left, one, "tag").commit();

getSupportFragmentManager().beginTransaction()
        .detach(one).commit();      // or .remove(), or .addToBackStack(null).remove()

getSupportFragmentManager().executePendingTransactions();

getSupportFragmentManager().beginTransaction()
        .add(R.id.right, one).commit();

Mas isso gera erro:

04-05 13:28:03.492: E/AndroidRuntime(7195): java.lang.RuntimeException: Unable to start activity ComponentInfo{com.example.trybackstack/com.example.trybackstack.MainActivity}: java.lang.IllegalStateException: Can't change container ID of fragment fragOne{40523130 #0 id=0x7f080000 tag}: was 2131230720 now 2131230721

Obrigado pela ajuda!