As mentioned in other answers, for the purposes of tides, the earth already has two 'moons', i.e. the moon and the sun. The difference in their gravity pull between the near side and the far side of Earth determines their influence on the tides. For nearby bodies this will be a much bigger difference.
The height of the tides however is much more determined by the shapes of the oceans and continents. There are places in the middle of oceans where there is nearly no tide at all. The strongest tides are at coasts where tides are funneled into a bay or similar body that has the right size to resonate with the pull of the moon. Tides in the oceans are more comparable to a bathtub on wheels that is being shaken and in which standing waves form, than with water flowing around the world following the moon's pull. So for a planet that is mostly water, with small continents that do not block the east to west flow of oceans like earth's continents do, the tides would be lower than on earth.
Another thing to note is that not just the oceans experience tides, the earth mantle does too. On the scale of the entire planet, the crust and mantle rock is flexible enough that you don't notice it. Earth tide is about a meter high. A closer moon will also increase the earth tide, which reduces the relative increase in ocean tide. Since water is lighter and much less viscous than rock I would still expect the ocean tide to increase if you put the moon closer, but I'm not sure about the details.
The best way I can think of for creating once-a-month very large tides would be to have a large moon in a very elliptic orbit. When it comes close to the planet you will have a single high tide (depending on how close the moon comes and how fast the planet rotates), when the moon is far away for a long part of its orbit, tides will be much smaller. One gotcha with such an orbit is that it is probably not stable over astronomic time scales, the tidal forces will act to circularize the orbit over time. So you can't have this configuration for the age of your planet if the planet is billions of years old as the earth is. But the moon could have been slung in this orbit by an encounter with another body a few 100000 or million of years ago. Given the previous paragraphs I'm not sure how high a tide this could create. My guess would be that you could still have higher tides, but you still need to make sure the continents are rather flat. My guess would be tides of a few hundred meters would be possible, but not kilometers. And your continents will need to be small and with big ocean inlets. Water still takes a lot of time to flood the land, and a big continent where the closest ocean is thousands of km away from the center would not have enough time to flood in a day.
Another note: a planet system with multiple large moons would also be unstable on astronomic time scales. One moon is fine, multiple small moons is also fine, but multiple large moons only works for a long period of time if the central planet is much larger, e.g. gas giants, so that the moons are small compared to their host planet.