postgresql DO UPDATE ON CONFLICT with multiple constraints

I have request that is a very similar to this problem postgresql ON CONFLICT with multiple constraints with only difference that I need to do DO UPDATE instead of DO NOTHING

CREATE TABLE test_table (
    col1 INTEGER,
    col2 INTEGER,
    col3 INTEGER,
    col4 INTEGER,
    CONSTRAINT col1_col2_unq UNIQUE (col1, col2),
    CONSTRAINT col1_col3_unq UNIQUE (col1, col3)
);

Is there any way to do something like this:

INSERT INTO test_table (col1,col2,col3,col4) values
    (?,?,?,?) 
    ON CONFLICT ON CONSTRAINT (col1_col2_unq OR col1_col3_unq) 
       DO UPDATE set col1 = EXCLUDED.col1

Now ON CONFLICT accepts only 1 unique constrain. Is there any options how to perfrom validataion for two set of unique fields before insert and update row if it matches any of them?