Would we be able to book the same flight if we did one ticket on ANA and one United? Are there hefty fuel surcharges or anything?

I am located in Florida. My ideal airport is PBI but can go FLL or MIA if that's better.

Dates are flexible. Was originally thinking November due to off-peak economy on American, but am now more open. Would love to stay longer but think I'd go broke buying things Having the other person apply isn't currently an option.

Thanks!