In the early 60's I was an interned at a group where two of the stations did exactly that: 50% total music overlap. Both were very top ratings performers in a market with over 30 stations back then.
Just want to add a little context, since many readers are likely not old enough to remember the competitive situation back in the stone age: In "the early 60's", the FCC had a 7-7-7 rule. A company could not own more than one single AM station, and/or one FM, and/or one TV station in any particular market. They could not own
any more than a maximum of 7 AM's and 7 FM's and 7 TV's (only 5 of which could be on the VHF band, i.e. channels 2-13) anywhere in the country. So no owner owned more than an AM and an FM in the same market.
And back then, FM was in its early stages, and garnered a fraction of the ratings that AM did, if for no other reason than the penetration of FM radios (especially in cars) was a small fraction of what was available with AM radios. Also, there was no Sirius, no XM, no HD, no smart phones or tablets, no streaming, no internet, no home computers, no portable computers. (Computers in that era were mainframes and filled rooms in government, large corporations and universities, and you had to belong to the "priesthood" to have access to one. Computer time was
very expensive.) Phone lines were all wired, and provided by a monopoly phone company, i.e. no competition. It was a very different environment.
So unless your internship happened in another country, it had to be a co-owned AM-FM situation, and the FM was of necessity very hobbled vis. the co-owned AM, regardless of the AM's class, directionality or signal strength.