For the record, any variation on the above should be classed as a novelty. But that's what we're here for, the arcane, the apocryphal, the obscure and the just damn strange. So it comes as no surprise that this one is so subtle, you might not even notice. To the make eye to parallel grooves look like a single groove. Two (or more) grooves start at the edge and spiral laps around the platter ending near the paper label.
Apocryphal reports place the practice with children's records in the 1950s on 78. This seems believable except the first patent I can find for it is in 1972. Lacking another strong citation I must go with the patent date. I dont rule it out an earlier date entirely, I just lack hard evidence.
You may already own records with parallel grooves. Two grooves will contain exactly half the music of one groove. So the duration will be a strong hint. The stronger evidence comes in the needle drop. As it's almost impossible to drop it in the exact same place, eventually you will land in one of the multiple grooves. If the grooves contain different songs, you'll confirm your thesis. Below is a short list of such releases:
Monty Python - Matching Tie and Handkerchief
I am Spoonbender - Teletwin - 12"
Psychic TV - Je Taime
Sonic Youth - 100% - 10"
LL Cool J - Goin' Back To Cali - 10"
Tool - Opiate EP (B side only)
Johnny Moped's - Cycledelic
Fine Young Cannibals - Good Thing 12"
The Secret Machines - The Road leads where it's led - 7"
None of Your Fucking Business - Escapes from Hell (2nd groove is silent)