That tool is an antique "breast drill" which might help
with your research.
I can't recall any "A" brand drill makers right now.
But everybody and his brother made those things.
It was also a common tool made by individual
craftsmen and tinkers. Most of these aren't marked.
I've never seen that drill mechanism. 2-speed models
are common, but I've never seen a 4-speed. Not sure
why you'd need 4 speeds.
My best guess is you have an early 1900s commercially
made tool that was home-modified by a clever inventor
to test out an idea. If the main body casting matches a
Stanley, Millers Falls, Fulton, etc. drill then it could be
enough evidence for that conclusion.
However, I don't recognize the main body casting.
It doesn't look like any 2-speed drills I know about.
That makes me think the drill came from the maker
like that. With nothing else to go on, I'd lean toward
that being a one-off prototype made by some home
inventor.
Then again, it may be a rare and valuable collectible.
Impractical, orphan designs and patent prototypes
are often collected. So you may want to consult with
antique tool experts in your region. Another resource
you might try is patent drawings from the late 1800s
to early 1900s.