Different coordinate systems in one map?

[RobertBasanta]

So I'm working on a project with data from a few different sources (as is typical) and am having an issue with my coordinate systems. Some of my features display in the correct location using WGS 1984 Web Mercator (auxiliary sphere) as the projected coordinate system and others, mainly those taken from CAD files, display correctly using NAD 1983 StatePlane Washington North FIPS 4601 (US Feet).

If I try to define one of the layers into a different coordinate system it relocates to a completely wrong location (i.e. using Web Mercator on the features taken from CAD moves them into the middle of the ocean). As I was under the impression it was better to limit the amount of coordinate systems used to decrease processing time/power I was trying to align everything into one coordinate system. Is this not feasible? Am I over thinking things trying to get to one coordinate system?

[DanPatterson_Retired]

You don't "define" a coordinate system as something else... you have to "project" it to the new coordinate system

[KoryKramer]

What Dan is getting at is that, from your description, the data already has a coordinate system defined.  If you use Define Projection on that data, you'll mess it up.  Instead, use Project—Data Management toolbox | Documentation 

[DanPatterson_Retired]

That is correct

Visually

/blogs/dan_patterson/2016/09/07/define-projection-vs-project-a-visual-guide