I'm working in a few targeted areas, and I wanted to project them all similarly. ROIs are on the order of 200 km x 200 km. For various reasons I'd like to use an equal area projection.

I like the Lambert Azimuthal Equal Area projection, but the only preset Lambert Azimuthal Equal Area projection in Arc is the North Pole Lambert Azimuthal Equal Area.

Are there any drawbacks to simply modifying the standard parallel and meridian of this projection for each target area?

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No, you shouldn't have any issues if you're using the data locally. The biggest issue you might face is if you want to use the customized coordinate reference system in a web map or application. Many want a "predefined" definition that has a well-known ID, AKA WKID like the infamous Web Mercator--EPSG:3857.

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