So you have data from a source, and he didn't keep a record of how he got the coordinates, and he's (pick one or more) dead, retired, nowhere to be found. And you have numbers but they don't fit the format of standard UTM grids, and when you try to run the numbers and get latitude and longitude you come out in the middle of Siberia (except when your data is actually from Siberia, in which case it comes out in downtown Burbank). Now what?
Pretty much every governmental entity advanced enough to draw a sketch map on a napkin has its own grid system. The reason is that a grid centered on the state or county fits the geography better than a grid that may be centered several degrees away. Also, depending on the shape to be covered, one map projection may work better than another. For New Hampshire, which is long in a north-south direction, the obvious projection is a transverse Mercator grid centered on 71 40 W. Now for the standard UTM grids, Zones 18 and 19 meet at 72 W, and the state would be split by two zones whose grids meet at an angle. Also the central meridian for Zone 18 is 75 W and the meridian for Zone 19 is 69 W, neither of which are anywhere close to New Hampshire. The standard UTM grid isn't well suited to New Hampshire, but a special grid centered on the north-south axis of the state works much better. For states that are long in the east-west direction, like Kentucky, a conic projection is better. The National Geodetic Survey standards for state grid systems specify that grids be based either on the transverse Mercator projection or the Lambert conformal conic projection. What's very nice from the standpoint of government agencies are that zone boundaries are defined by state and county lines, not latitude and longitude. So towns and counties are never split.
Why local grids? They're more accurate. The standard UTM grid is accurate to one part in 2500. That is, if you measure a distance on the map in terms of the grid, and then measure it on the ground, you could be off by 1/2500, or about two feet in a mile. No biggie for targeting artillery (since the UTM system was started by the military) but possibly big trouble if you're plotting right of way for a road and the guy whose property is on the wrong side of that two feet is litigious. So the state plane systems try for accuracy of one part in 10,000 (six inches per mile). They do that by having smaller zones so the projection surface fits the earth more snugly, and by having the projection surface better centered on the state.
It's possible to have even more specific local grids. Wisconsin and Minnesota (and possibly other states) have county grids. These use not only the projection best suited to the shape of the county, but take topography into account as well. For a datum (model of the earth's shape) they use not sea level, but an ellipsoid matching the average elevation of the county. And if the county has an overall topographic slope, the grid will be shifted so that the cylinder or cone mapping the county provides the closest fit to the county topography. Wisconsin shoots for (and mostly gets) accuracy of one part in 30,000 for the county grids in rural areas and 1 in 50,000 or 1-1/4 inches in a mile in urban areas. For example, one grid covers four counties in southeast Wisconsin along the Lake Michigan shore. The central meridian isn't at the longitude that best fits the shapes of the counties, but a bit farther east. The shift optimizes accuracy in the urban areas, which are all along the lakeshore.
So if you have odd looking numbers, you may have a state or county grid. The agencies most likely to be able to provide information are your State Department of Transportation, State Surveyor, or State Geological Survey. Also, early implementations of state plane coordinate systems used feet for their unit of measure, not meters, and surveyors still work a lot in feet. So if meters don't work, try feet.
Also, if the map that was used is a privately published map, like say for a guidebook, the grid may be an entirely arbitrary one defined by the publisher. I once got an inquiry from someone looking at data from Mexico, and finally figured out the map had 0,0 at Tijuana, the far northwest corner of Mexico, and measured south and east from there.