That's a beautiful 'prewar' M1903 in the original Steyr factory takedown version.

I see two things that don't seem to belong there, however. The side safety is of a later model / type (M1900, '03, '05, '08, '10, '24 had wing safety only), and I've never seen a Steyr built MS takedown with that additional knurled screw that threads into your receiver from the underside.

Was that 'bottom screw' added when it was rebarreled? My M1910 takedown (proofed 1922) has the 'lug' threaded, but the stock is solid beneath as are all others I've seen. The 'Osterr. Waffenfabr: Ges. Steyr' stamping indicates that yours was manufactured no later than 1926. When was it proofed?

'New shotgun type side slide safety' (say that three times fast?) on a 1952 model (from 1954 Stoeger catalog):

Fullstocks are held together thus;

Steyr 'factory takedowns' relied on the groove at the tang, the forend pin, and the lever catch fore of the triggerguard.

MS parts, from the '39 Stoeger:

The full page. No side safety, no 'big screw':

The stock modification is unfortunate. You've lost this: