I have a couple of questions in regards to the Power battery.
1-You cannot have more than one of the same construct attached?
2-Can Call-ins be given constructs?
3-Can Bystanders be given constructs?
4-Can a character already equipped with a special object be given a construct?

1. Correct. The Battery calls for "distinct constructs" meaning all different.

2. No. Giving a character a construct also assigns them the Battery. Call Ins cannot be assigned resources.

3. Yup.

4. Also yup. Constructs are not objects.

To note for #1, back when they were new, WK ruled that 2 same constructs of different colors were still considered the same... so no blue nurse and green nurse, for example.

However, if you look at the passage in its rules, that only applies to when you're putting them on during force construction... you could use the swapping power on the battery to swap a construct on it for another copy of one you have on it.

Did not consider that. Thanks!

It takes potentially a few turns as the power is only on certain clicks, but if you really need 2 of one of them on it, you can get it with the right setup.