glob returns a list: why not just run it multiple times and concatenate the results?

from glob import glob
project_files = glob('*.txt') + glob('*.mdown') + glob('*.markdown')

Glob uses the fnmatch module at the back end, maybe you can just use that directly yourself? Here's an approach with the checking out in a function to keep the body of your code cleaner:

eg.

import sys
import fnmatch
import os


def filter_files(file_list, ext_list):
    for file in file_list:
        for ext in ext_list:
            if fnmatch.fnmatch(file, ext):
                yield file
                break

BASE_PATH=sys.argv[1]

EXTENSIONS= "*.jpg", "*.png", "*.gif"

for dirname, dirnames, filenames in os.walk(BASE_PATH):
    matches = list(filter_files(filenames, EXTENSIONS))

If you need to use pathlib.Path.glob()

from pathlib import Path
def get_files(extensions):
    all_files = []
    for ext in extensions:
        all_files.extend(Path('.').glob(ext))
    return all_files

files = get_files(('*.txt', '*.py', '*.cfg'))

Here is an example from http://web.purplefrog.com/~thoth/blender/python-cookbook/image-to-material-node.html :

def image_for(fname):
    candidates = [ img for img in bpy.data.images if img.filepath == fname]
    if len(candidates)<1:
        return bpy.data.images.load(fname)
    else:
        return candidates[0]

def node_of_type(nodes, type):
    for node in nodes:
        if node.type == type:
            return node

def mission1(fname):

    mat = bpy.data.materials.get("material")
    if mat is None:
        mat = bpy.data.materials.new("material")

    mat.use_nodes = True
    nodes = mat.node_tree.nodes

    n1 = node_of_type(nodes, "TEX_IMAGE")
    if n1 is None:
        n1 = nodes.new("ShaderNodeTexImage")

    n1.location = (-200,0)
    n1.image = image_for(fname)

    bsdf = node_of_type(nodes, 'BSDF_DIFFUSE')

    mat.node_tree.links.new(bsdf.inputs[0], n1.outputs[0])

    coord = node_of_type(nodes, 'TEX_COORD')
    if coord is None:
        coord = nodes.new('ShaderNodeTexCoord')
    coord.location = (-400,0)

    mat.node_tree.links.new(n1.inputs['Vector'], coord.outputs['UV'])

    return mat

mat = mission1("/home/thoth/art/dancing-bear/bear384.png")
bpy.context.active_object.data.materials[0] = mat

You could create a list and loop over it

exten_to_find = ['.pro','bd3','.mysql']

you could format like this for iteration

files = glob.glob("**/*{x}*.{y}".format(x = myStr, y = extension_toFind), recursive = True)

This worked for me:

for f in path.glob("*.[jpeg jpg png]*"):
    ...

As a reference fnmatch:

[seq] matches any character in seq

And in Path.glob:

Patterns are the same as for fnmatch, with the addition of “**” which means “this directory and all subdirectories, recursively”.

Edit:

Better way would be something like:

*.[jpJP][npNP][egEG]*

I didn't know the proper POSIX-compliant way of doing it. The previous way will match files like ".py" because the brackets match any letter in whatever order.

This way should match "jpeg", "JPEG", "jpg", "JPG", "png" and "PNG". It also matches formats like "jpegxyz" because of the "*" at the end but having the sequence of brackets makes it harder to pick up other file extensions.