Adding one aspect here because I received feedback on this - within an EA contract there is the option for "organization-wide" licensing (aka "company wide") - which has the benefit of getting a better pricelevel, but also has contractual obligation to license e.g. all internal staff with the same set of licenses via the EA ("standardize" ). While this does not change the technical ability to also add CSP licenses, please be aware that in some agreements it might be required to license additional internal users during a true-up.
I'm not an expert on EA agreements, so I cannot say how exactly those terms look like - this is just a general reminder to check the contracts on this. My first answer above was only refrring to the technical ability to do this.
More on the ability to combine different licensing channels in one customer tenant: https://docs.microsoft.com/en-us/partner-center/multichannel
How to invite the existing (EA) customer is not different as inviting other customers with existing tenants:
