The stock, of course is extensively "sporterized". From pictures, metal parts look to be all there - looks like the military front sight, so barrel was not cut off. There will be at least 4 serial numbers - on bolt handle, on receiver, on barrel and on the front face of the rear sight - when ladder is standing up. I have one "E" with cut down stock that also has the receiver serial number stamped in the barrel channel. Because your receiver is marked "RE", it was made at the Remington factory in first half of WWI - the only time they were made - so would have left that factory with pretty much all the 60 or so parts (except screws and coil springs) with a small "R" stamp - but often swapped out in service, or after service - many, but not all, parts from an "E" or a "W" P14 would fit, or at least could be made to fit well enough to work. Looks like an Asterisk or a Star stamped below the RE - look into rear of chamber area - the rear end of the barrel will have a groove cut part way around the chamber area - the bolt should also have the same asterisk, if the serial numbers do not match - was the difference between the Mark I and the Mark I* versions - left bolt lug is different. Some of us have been looking for years for original WWI military P14 stock and hand guards - just do not see them available - is similar to, but not identical to, an M1917 stock, but they seem just as scarce. Contractors in Britain also made replacement stocks during WWII for the British re-build program that they did then. Numrich (gunpartscorp) does sell reproduction stocks and hand guards. Over past about 4 years I have bought maybe 8 or 9 P14 and M1917 like that one - paid $60 for one with totally rotted out barrel that a bullet will drop right through without touching, up to $300 for nice Winchester P14 that was more or less all there and more or less all "matching", but with cut down sporterized stock.
Your pictures make that look like someone's favourite hunting rifle - would be an excellent moose, deer or black bear rifle, for sure, so bore condition would be quite important in arriving at a value for it, as a "shooter".