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Is "不特定多数"する a slang term that means to date more than 1 person at the same time? For example, Tanaka-san would date person A on Monday, person B on Wednesday, then person C on Friday and Saturday. "田中くんは不特定多数よくやる人だよね。うらやましいなああ。"
This phrase was used (by me at least) a long time ago, and my memory is poor. It seemed to get my intended meaning across... but I don't remember native speakers saying it, yet its a very weird thing to say. I've no idea how I might have "learned" the phrase.
不特定多数 is a stiff set phrase typically used in legal or other business-related contexts. I don't think it has a slangy usage like you mentioned, and 不特定多数(を)する doesn't make sense to me. The most common way to say "dating more than one person" is 二股【ふたまた】をかける (or 三股, 四股, ...).
While we don't normally say "不特定多数する", the word "不特定多数" is fairly commonly used to talk of promiscuity or indiscriminateness in romantic/sexual relationships, as in "不特定多数の相手と関係をもつ". So quite possibly you got that expression through this association.
If I were to hear someone say "不特定多数する" I'd probably think (after a moment's pause) it's a grammatical innovation (especially in the mouth of a fluent speaker) or simple error (especially in the mouth of a less-than-fluent speaker), but under the right set of conditions, the intended meaning "date more than 1 person at the same time" may easily get across.
