There exist several abilities that have the text similar to, this effect lasts while you maintain concentration (as if you were concentrating on a spell). One such example is the Bard College of Glamour: Mantel of Majesty abililty.

At 6th level, you gain the ability to cloak yourself in a fey magic that makes others want to serve you. As a bonus action, you cast command, without expending a spell slot, and you take on an appearance of unearthly beauty for 1 minute or until your concentration ends (as if you were concentrating on a spell). During this time, you can cast command as a bonus action on each of your turns, without expending a spell slot.

Another example is the Cleric Trickery Domain: Channel Divinity: Invoke Duplicity ability.

Starting at 2nd level, you can use your Channel Divinity to create an illusory duplicate of yourself.

As an action, you create a perfect illusion of yourself that lasts for 1 minute, or until you lose your concentration (as if you were concentrating on a spell).

While you are concentrating on maintaining such an ability would you also be able to maintain concentration on a spell that requires concentration?

There does not seem to be any RAW that limits this however the limitation around concentrating on a second spell exists which may suggest that the intent is that a character cannot concentrate on 2 effects at the same time unless explicitly stated.

There exist several abilities that have the text similar to, this effect lasts while you maintain concentration (as if you were concentrating on a spell). One such example is the Bard College of Glamour: Mantle of Majesty ability.

At 6th level, you gain the ability to cloak yourself in a fey magic that makes others want to serve you. As a bonus action, you cast command, without expending a spell slot, and you take on an appearance of unearthly beauty for 1 minute or until your concentration ends (as if you were concentrating on a spell). During this time, you can cast command as a bonus action on each of your turns, without expending a spell slot.

Another example is the Cleric Trickery Domain: Channel Divinity: Invoke Duplicity ability.

Starting at 2nd level, you can use your Channel Divinity to create an illusory duplicate of yourself.

As an action, you create a perfect illusion of yourself that lasts for 1 minute, or until you lose your concentration (as if you were concentrating on a spell).

While you are concentrating on maintaining such an ability would you also be able to maintain concentration on a spell that requires concentration?

There does not seem to be any RAW that limits this however the limitation around concentrating on a second spell exists which may suggest that the intent is that a character cannot concentrate on 2 effects at the same time unless explicitly stated.