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Snap points to lines based on attribute matching

I have two large datasets - monitors (points) and pipelines (polyline).

The monitors have an attribute "Pipeline Name", and the pipes have an attribute "System", but the unique values of the two fields are the same.

Some of the monitors are located in areas where they may snap to the wrong pipe system if the vanilla snap tool is used.

Is there a way to snap the monitors to the pipelines, but only if the attributes match? The attribute field names are easily manipulated if that is an issue.

The only way I can visualize doing it would be to break down each shapefile by the attribute (Pipeline Name for the monitors and System for the pipes), then load those files individually into ArcMap and snap them. With a large number of named systems (100+), though, this seems like a lot of unnecessary processing.

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