Javascript find objects that contain matching elements from arrays in another object

I have two objects:

const people = [
{
    name: "Dave",
    fruit: ["apple", "pear"],
    veg: ["asparagus", "peas"]
},
{
    name: "Frank",
    fruit: ["mango", "banana"],
    veg: ["sweetcorn"]
},
{
    name: "Alice",
    fruit: ["mango", "peach"],
    veg: ["asparagus"]
}];

const demographics = {
  fruit: ["apple", "mango"],
  veg: ["asparagus"]
}

I would like to find which ‘people’ like the fruit ‘apple’ or ‘mango’ and the veg ‘asparagus’, as defined in the ‘demographics’ object, like so:

[{
    name: "Dave",
    fruit: ["apple", "pear"],
    veg: ["asparagus", "peas"]
},
{
    name: "Alice",
    fruit: ["mango", "peach"],
    veg: ["asparagus"]
}]

I’ve been staring at this all day and am not advanced enough to dig into objects like this. Can anyone help? If possible, I would like to use underscore, but not essential.