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I'd like to create a custom CRS that meets some requirements I need for a project. I've spent a lot of time looking for all existing projections consulting for example this site: https://map-projections.net/singleview.php, but I'm bounded to those available on GIS software (I would have been satisfied with the Apian II projection, but is not available either on QGIS or on Proj library).

I came across the tool Flex Projector which allows modifying the length and distance of parallels from the equator, following the same rule the Robinson projection is based on, according to this table http://www.radicalcartography.net/projections/robinsontable.html

Starting from the Robinson projection here below:

enter image description here

I'd need something more like this, with these parameters:

enter image description here

From other questions I saw on this topic it seems difficult to create a custom CRS from scratch, not based on an already existing registered projection, so my question is: is it possible to modify the math behind an existing projection based on the information available on the WKT definition?

PROJCRS["Sphere_Robinson",
    BASEGEOGCRS["Unknown datum based upon the Authalic Sphere",
        DATUM["Not specified (based on Authalic Sphere)",
            ELLIPSOID["Sphere",6371000,0,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["Sphere_Robinson",
        METHOD["Robinson"],
        PARAMETER["Longitude of natural origin",0,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Not known."],
        AREA["World."],
        BBOX[-90,-180,90,180]],
    ID["ESRI",53030]]

p.s I know there are many projections that resemble the projection I look for but for one reason or another, they often don't meet the requirements I need.

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