’'Lay claim to the interest of…’'?

Dear Everyone,

I’d like to find the proper phrase which will express that a many-sided and varied written work can lay claim to the interest of multiple audiences (that is, that we can expect it to be appealing for and hold the interest of multiple audiences).

I suspect "lay claim for" is not the right wording – could you, please, tell me what could be used instead?

Thank you!