I have a single-engine land PPL. I'm looking at getting training in a multi-engine seaplane. Does the fact that I already have a land airplane rating allow me to fly a multi-engine land plane?
(I did find this question, which seems to indicate the answer is "no", but I want to make sure.)
I think the answer to your question is best served by looking at the Private Pilot Airplane - Airman Certification Standards (PVT ACS). Below, from page A-14 of the PVT ACS, you can note that some of the Areas of Operation and Tasks that you must be tested on in order to become rated in a Multiengine Land airplane (based on the specifics of your question) are different than you would be tested on while obtaining your Multiengine Sea rating.
So, in other words, it takes training and testing in those Areas of Operation/Tasks that are different between an Airplane Multiengine Sea and an Airplane Multiengine Land airplane. The rating to fly both Multiengine Sea and Multiengine Land airplanes will be noted separately on your pilot certificate once you have completed the Certification check in both classes of Multiengine airplanes. The same procedure would apply to your top-line question with respect to having the rating to fly a Single-engine sea airplane (refer to the PVT ACS, page A-13).
From page A-14 of the Private Pilot ACS (linked above):
Also, as a note, look at 14 CFR 61.31(d): (emphasis is mine)
Aircraft category, class, and type ratings: Limitations on operating an aircraft as the pilot in command. To serve as the pilot in command of an aircraft, a person must-
(1) Hold the appropriate category, class, and type rating (if a class or type rating is required) for the aircraft to be flown; or
(2) Have received training required by this part that is appropriate to the pilot certification level, aircraft category, class, and type rating (if a class or type rating is required) for the aircraft to be flown, and have received an endorsement for solo flight in that aircraft from an authorized instructor.
Airplane is the "category" and Multiengine Land and Multiengine Sea are different "classes."