Here is a method that seems to work just fine.
French Pressing allows the coffee to sit in the water for however long you like it to, to extract more flavor from the grinds.
Messy to clean up, also dust gets through the metal screen.
However, you can pour the coffee through a paper filter after this process is completed.
A Percolator is fine for allowing water to continually drip through the grinds, again for however long you like, but it BURNS the coffee.
Here is a method that I just used today and it works great. You can almost get the best from both worlds.
I used my Hamilton Beach Cone Drip Coffee Maker. It has an automatic stop when the Carafe is removed as many coffee makers do.
If you swing out the Basket approx. 1/2 inch, the coffee does not drip through the bottom.
Important, this coffee maker has one hole up above for the hot water drip into the basket from. If there are multiple holes spread out around the entire circumference of the top, you could have water dripping all over the place. So please make sure that if you swing out the basket on your coffee maker, that the hot water still drips directly into the basket and that the coffee does not drip through the bottom of the basket until you push it back into place.
So, here is my method.
Place the desired amount of coffee grinds into the basket and pour the desired amount of water into the reservoir.
Now, swing out the basket just enough so that you can see into the basket. Turn the coffee maker on.......Watch the water as it fills into the grinds in the basket. When the water in the basket rises to about a half inch below the top of your filter, turn off the coffee maker. Now, let the water sit in the basket for 5 minutes. More or less is up to you.
I did this with 48 ounces of water (8 6oz. cups of coffee) and 8 tablespoons of coffee.
(Use a measuring Cup.) (10 cups on a Mr Coffee Carafe is only 8 cups on a Melita Carafe.)
Now push the basket back into place and let the coffee drip into the Carafe. When drained, do this process again. I did this 3 times and then I just allowed the remaining water to drip right in the basket and into the carafe.
This method allows you to have coffee grinds submerged in the water for however long you like. You don't have to go through this process for the entire brew either. You can do it for only the first or second basket fills or through the entire process.
You'll get more flavor out of the grinds like french press.
You can also do this by removing the basket and placing it over the carafe on the counter top. Pour your hot water into the Basket........Let it sit. Then depress the lever underneath the basket to release the stopper and let the coffee drip into your carafe. Then pour more water into the basket.
Just like using a Melita portable coffee brewer with the cone basket that sits over a carafe or the smaller one that fits over a cup. Just find a way to keep the hole at the bottom close until you decide to allow the coffee to drip out.
NO dirty coffee grinds to clean out of the bottom of the French Press' screen and bottom of the Glass.
Give it a try. You have nothing to lose. Just improvise a little and you can do a lot of amazing things that are so simple.