I apologize if this is a little long, but I need to give the backstory before my questions.
Back in about '74 my dad sent me to pick up a bicycle a friend was giving him. It was an old bike- sewn tires, etc. I want to say it was either orange or lime green, but I really don't remember. Dad put some regular road tires and rims on it but he didn't ride it much because it was too tall for him.
He was a Honda motorcycle mechanic starting in about '66. In the early '80s his shop started carrying bicycles and parts. Since a lot of people buying the bikes upgraded the components at the time of purchase he had a lot of new/take-off parts laying around. He decided to upgrade the old bike we had. He had the original paint removed and a semi-custom paint job applied.
At one point he wanted to replace the crankset but could not find a single set that fit the bike. He took it to a local bike shop. This is where it gets interesting. The old man who owned the shop looked at the bike and said it was an old Schwinn Paramount made back in the '50s. He found a crankset and installed it, and it fit perfectly. He had a second crankset so dad just bought both. I still have the second in the box.
Much later I had someone tell me it wasn't a Paramount. I think he said the frame gussets were wrong for a Paramount. On the frame head I found a couple of, well not really nuts, but close enough, that hold the steering head bearings in. They are marked Olmo in raised letters, so I started thinking that is was an old Olmo. I looked for a serial number and found one on the seat riser part of the frame- not under the crank. It is A-327. I tried looking up that number on a serial number page for both Olmo and Schwinn. I didn't find one on the Olmo site but did on the site for Paramounts.
Any decals or badges were apparently removed by the guy who painted it. It is a steel frame- I think chromed. A magnet will stick to it. It is lighter than my aluminum Raleigh.

Now my questions.
Can a crankset for a Paramount fit an Olmo? I don't know how specific they are.
Would a Paramount have head bearing nuts from Olmo?
Is what I am taking to be a serial number actually a serial number? Why would it be on the seat frame and not the bottom of the frame under the crank?

I am trying to figure out what it is, mainly out of curiosity. Since nothing really is original other than the frame it wouldn't have any collector value. I does ride very well- smooth and fast.
Sometime I might decide to restore it to near original, but the question is to an original what?

I also have a couple of Raleighs from back in the early '80s I will ask about in another thread- an aluminum Technium and a steel Grand Prix. Dad paid about $400.00+ for each, and that was dealer cost.

I know you need pics to help. Please tell what specifically you need pics of other than just overall pics of the bike.

Thanks,
Jim