With gzip files, you can simply concatenate the files together, like so:
cat file1.gz file2.gz file3.gz > allfiles.gz
Per the gzip RFC,
A gzip file consists of a series of "members" (compressed data sets). [...] The members simply appear one after another in the file, with no additional information before, between, or after them.
Note that this is not exactly the same as building a single gzip file of the concatenated data; among other things, all of the original filenames are preserved. However, gunzip seems to handle it as equivalent to a concatenation.
Since existing tools generally ignore the filename headers for the additional members, it's not easily possible to extract individual files from the result. If you want this to be possible, build a ZIP file instead. ZIP and GZIP both use the DEFLATE algorithm for the actual compression (ZIP supports some other compression algorithms as well as an option - method 8 is the one that corresponds to GZIP's compression); the difference is in the metadata format. Since the metadata is uncompressed, it's simple enough to strip off the gzip headers and tack on ZIP file headers and a central directory record instead. Refer to the gzip format specification and the ZIP format specification.
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