Many years ago there was a(antenna?) company that sold an antenna switch that allowed switching vertical, horizontal and connecting both together.
It was pretty heavy, but I think the circuit for both was power limited.
Jo Gunn sold the spider-looking antenna, with vertical and horizontal for years and is lighter weight and catches less wind that the cross.
The Jo Gunn cross antennas came out after amateur radio allowed no-code techs on 10 meter SSB.
The idea was mostly to use vertical for CB radio and to tune horizontal for 10 meters.
I had a neighbor that had the Jo Gunn 4-element star / spider on a huge tower.
He spent a ton of money having it put up with 4 yards of concrete in his yard.
I was surprised he chose the 12 foot long 4 element over the 5 element, for the money he spent.
I messed around with co-phasing different cross antennas.
I would think the power and the receive would be cut in half on each one.
For tuning, tune one with the other disconnected.
Then tune the other one while leaving the first tuned one still connected.
What this may do though, is allow using the first one tuned alone, but the second might not in tune by itself.
If you tune one at a time, through the co-phasing harness, you can each one alone, but together the tuning might be a bit off, but maybe no enough to make a difference.
When tuning separately, use the co-phasing cable, but only with each connected separately.
Then connect both to the co-phasing cables.
The JoGunn initial tuning is usually pretty close, but the anodized finish on the aluminum tubing doesn't always make good connections.
The issue I had with Jo Gunn years ago, was the screws were not stainless steel and quickly rusted and the holes for them in the tubing was often undersize and the screws would break while tightening them.
The antennas worked well, but I'd change the screws for stainless steel ones and make sure all of the holes for them are larger enough, though the holes are supposed to be a bit smaller than the screws.
Years ago, Antenna Specialists sold a 5 element cross antenna on a 22 foot boom.
I only ever saw one in use.