Execute multiple map iterators in javascript

I want to understand once concept related to the map iterator in javascript. I want to execute multiple map iterator and I have came up with the below solution.

await Promise.all({
    arrOne.map(async first => {
         arrTwo = //call another await operation
        arrTwo.map(async second => {
            arrThree = //call another await operation
            arrThree.map(async third => {
                //return await operation and result
            })
        })
    })
})

What I want to achieve is to process the data in the parallel approach which I think through Promise.all we can achieve. I want to know if this is the good approach.

Also I want to process a large dataset. Will the above approach works because I was also thinking to process the data in batches.