Sumerian was an isolate as far as can be determined now (since it was uniquely a literate society), and has no living relatives. I’ve never seen any philologist argue otherwise. It was agglutinative, but its morphemes were not carried on anywhere else; Turkish, Korean, and Japanese are sometimes grouped together (particularly Turkish and Korean), and all are agglutinative, but other agglutinative languages aren’t related to any others, or are in small families that are unrelated to other agglutinative families.
Here’s one Finno-Ugric chart:
http://www.helsinki.fi/~tasalmin/fu.html
Used to be folks thought the Sa'ami were simply Suomi and Swedes who'd wandered away from camp. We now know they are genetically different sufficiently to identify them as "genetic isolates".
The Sa'ami languages certainly drew on the neighboring tongues for vocabulary, but not the grammar. BTW, there is a grammatical construct in the Germanic languages that must necessarily be a derivative of Sa'ami, and that's enough to demonstrate that they should not be classed with the Finno-Ugric subgroup.
The Japanese and Korean languages necessarily draw on the Yakut/Sakha language of their 6th century AD conquerers! That language is pretty much the same as the Yakut/Sakha their ancestors spoke in Nepal from about 500 BC to 200 AD when they got kicked out by the Hindus. They returned to Yakutia, encountered some seriously negative climatic changes circa 535-41 AD and fled East toward the much warmer East Asian maritime (Korea and Japan).
The Yakut have some genetic information in common with the Sa'ami in the East that they don't share with any other group, not even the Mongol or Hun populations.
Note, although there is a broad trend toward populations speaking similar languages sharing lots of ancestors, that's not always the case. In the earliest periods 8,000 years ago, there's not even any reason to believe that the ethnic groups living in any particular region of the world are the same as the people who left signs of civilization behind.