'already suggests' is correct and usable in written English.
It is used to indicate that something has been suggested or is implied prior to making another statement. For example: The fact that he has no job already suggests that he is struggling financially.
You may have an idea that already suggests characters of a particular age.
That already suggests enough drama for a box set series on Sky Atlantic, but there's more.
Miss Sheikh's experience already suggests the Supreme Court is determined to get tough with delinquent witnesses.
But evidence already suggests that the review will have an impact on school teachers and the police.
This natural academic rhythm already suggests that Fresh Meat should be good for at least three strong series, and perhaps beyond.
Tweddle undoubtedly achieved her success through years of hard work and natural talent, but for me her name already suggests something bendy and flexible like a pipe cleaner.
In 358 he invaded Paeonia, and then he defeated the Illyrians decisively, in a battle that already suggests a master of war.
Since wholesale importers enjoy big economies of scale over retail consumers, this already suggests that trading costs may have an important role in the matter.
The documents entitled "Mastering the Internet" already suggests GCHQ are scooping vast amounts of online and telephone traffic without any form of public acknowledgement or debate.
But that already suggests a mellowing from the anger that first earned him literary renown in the late 60's and early 70's as a vociferous antiwar poet.
Once again, it needs stating because it can't be stated too often: despite the desperate efforts of the National Rifle Association to prevent research on gun violence, the research has gone on, and shows conclusively what common sense already suggests.
