Would layering Work?

Hi people, I am wondering is there a possibility or better way to make two recordings sound like they were record at the same time when they are really a instrumental recording recorded one day and then a vocal recording recorded another day...

Is it possible to do this...

I am wondering would a layer of the instrumental

Then a layer of vocals

Then a layer of  of instrumental

Make it sound less like one was just laid over the top or would it just still sound the same as if I had just laid a instrumental over the vocals?

Just wanting to do my best so that the vocals don't sound like a voice over....

And people don't say hmm..."why does it sound like the instrument is covering up the vocal?"

?

Thanks for your advice and possibly help!