You have different methods

Here is this one with the losanges...
one by one
Scale 3D the losange from center for overpass the 4 segment
Intersect (Trim) the verticals (or oriented, Normal etc..) with the 4 segments around the losange
PolyLine the 4 points



then...

With your 4 facets (FlowExtend Srf ? Very cool! )
https://moi3d.com/forum/index.php?webtag=MOI&msg=9747.21

Make boolean like this

Select 1 2 Call Boolean Isect 3 4 as "second object set"
(you can of course take more facets in a pass - in your case 7 vertical Quads selection)
that gives the 4 points for PolyLines then Planar...erase not wanted ...etc
But it's an hard work because only "manual"! ;)

For more easy use
Copy Move facets and then process else all will be a mess above the original! ;)
And be more precise than me on these speedy test! (top facet is not well aligned on the b corner! :)