def METHOD_NAME(versions=None, supplied_platform=None):
    """Return a list of supported tags for each version specified in
    `versions`.
    :param versions: a list of string versions, of the form ["33", "32"],
        or None. The first version will be assumed to support our ABI.
    """
    supported = []
    # Versions must be given with respect to the preference
    if versions is None:
        versions = []
        version_info = get_impl_version_info()
        major = version_info[:-1]
        # Support all previous minor Python versions.
        for minor in range(version_info[-1], -1, -1):
            versions.append(''.join(map(str, major + (minor,))))
    impl = get_abbr_impl()
    abis = []
    abi = get_abi_tag()
    if abi:
        abis[0:0] = [abi]
    abi3s = set()
    for suffix in get_all_suffixes():
        if suffix[0].startswith('.abi'):
            abi3s.add(suffix[0].split('.', 2)[1])
    abis.extend(sorted(list(abi3s)))
    abis.append('none')
    platforms = []
    if supplied_platform:
        platforms.append(supplied_platform)
    platforms.append(get_platform())
    # Current version, current API (built specifically for our Python):
    for abi in abis:
        for arch in platforms:
            supported.append(('%s%s' % (impl, versions[0]), abi, arch))
    # abi3 modules compatible with older version of Python
    for version in versions[1:]:
        # abi3 was introduced in Python 3.2
        if version in ('31', '30'):
            break
        for abi in abi3s:   # empty set if not Python 3
            for arch in platforms:
                supported.append(("%s%s" % (impl, version), abi, arch))
    # No abi / arch, but requires our implementation:
    for i, version in enumerate(versions):
        supported.append(('%s%s' % (impl, version), 'none', 'any'))
        if i == 0:
            # Tagged specifically as being cross-version compatible
            # (with just the major version specified)
            supported.append(('%s%s' % (impl, versions[0][0]), 'none', 'any'))
    # Major Python version + platform; e.g. binaries not using the Python API
    for arch in platforms:
        supported.append(('py%s' % (versions[0][0]), 'none', arch))
    # No abi / arch, generic Python
    for i, version in enumerate(versions):
        supported.append(('py%s' % (version,), 'none', 'any'))
        if i == 0:
            supported.append(('py%s' % (version[0]), 'none', 'any'))
    return supported