Gaming laptops with an MXM format GPU typically starts at $1,400.
A MXM format GPU alone generally will cost at least $400; I have seen MXM GTX 1080 8GB GPUs selling for as much as $1,500 alone.
Additionally, you are not going to find a Core i7 CPU in a new $400 or less laptop. You may be able to buy used laptop with a 3rd generation Core i7 CPU in that price range. If you are looking for the best laptop for less than $400, then you need to settle on the following Acer laptop with a Core i3-7100u and Intel HD 620 graphics core. AMD has nothing in the price range that can compete with the power of the Core i3-7100u and the performance of the Intel HD 620.
The MxM laptops are veeery rare, and normally are expensive, also the MxM technology almost never worked and had a lot of problems that makes it very unreliable to upgrade a component. Even if you get a laptop you have posibilities that you could never upgrade it.
Stil, if you want it i seriouly doubt that you could find a proper i7 without MxM for less than 400$ not to talk to find one with MxM, probably you would need to triple the amount of money to find one.
With 400$ as limit the only options i see are to find one i7 one or to generations old (without a gamming Gpu ofc) or try to seek a second handed MxM one, but well for that price probably it will be deteriorated or have severe flaws.