Several months ago I learned from an answer on Stack Overflow how to perform multiple updates at once in MySQL using the following syntax:
INSERT INTO table
There is no simple command to do it.
The most correct approach is to use function, like the one from docs.
Another solution (although not that safe) is to do update with returning, check which rows were updates, and insert the rest of them
Something along the lines of:
update table
set column = x.column
from (values (1,'aa'),(2,'bb'),(3,'cc')) as x (id, column)
where table.id = x.id
returning id;
assuming id:2 was returned:
insert into table (id, column) values (1, 'aa'), (3, 'cc');
Of course it will bail out sooner or later (in concurrent environment), as there is clear race condition in here, but usually it will work.
Here's a longer and more comprehensive article on the topic.