Setting up more than one HSA for spouses

[Guest Levetech]

My wife and I both work for the same company and we have a HDHP with HSA as our option. Our employer is offering an HSA contribution of $400 for individuals and $800 for all other coverages (ee + spouse, ee + kids, family.) I am thinking that it's in our best interest to split the plan where I will cover the kids ($800 ER contribution) and she will get her own coverage ($400) contribution. The contribution we have to pay is actually cheaper that way as well - rather than me covering the family.

I have a few questions about this approach:

1.) If we each decided to contribute to our own HSA's, would we be able to contribute the maximum for both of us? In other words, could she put away the Max individual contribution while I put away the max family contribution?

2.) I understand that our out of pocket max could be much higher in this approach if we both have significant medical costs but are there any other downsides to this approach.

I appreciate your thoughts.