I'm slowly putting a Stevens Marksman .22 together and got a takedown screw but it only goes in about 1/3 to maybe 1/2 the way in. The screw appears to be 5/16X32 but there is just something not working correctly. I have some other 5/16X32 screws that work ok but comparing the two and the threads seem to match but those on the takedown screw actually appear fatter.
Do I need to get me a 5/16X32 die to get this working or am I wrong about the takedown screw thread size.

you are vedry close. I found an old thread that first refers to the Marksman takedown threads. The first replier says it's a 5/16x28! I don't know which is messed up -- the takedown screw or threads in the receiver so I'll get both tap and die. You have darn good eyes to be able to count those little threads.
Old thread I found
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If it is the same thread as all the Favorites.
Then its the Very ODD Stevens thread of .300 x 30 tpi