It’s right there in JDK! Quoting JavaDoc of SequenceInputStream:

A SequenceInputStream represents the logical concatenation of other input streams. It starts out with an ordered collection of input streams and reads from the first one until end of file is reached, whereupon it reads from the second one, and so on, until end of file is reached on the last of the contained input streams.

You want to concatenate arbitrary number of InputStreams while SequenceInputStream accepts only two. But since SequenceInputStream is also an InputStream you can apply it recursively (nest them):

new SequenceInputStream(
    new SequenceInputStream(
        new SequenceInputStream(file1, file2),
        file3
    ),
    file4
);

…you get the idea.

See also

• How do you merge two input streams in Java? (dup?)