One of the design methods I like to use when coming up with game ideas is creating a mind map. A mind map is a way of visually presenting concepts and connecting the dots together with various info and ideas. It also helps organize your thoughts and potentially create even more possibilities for themes and gameplay.
As an example, I am going to show a mind map I constructed with the title Galaxy Dungeon, an action escape the dungeon game that includes themes/genres of assassins, physics, zero-gravity and puzzles:
I took some creative liberty and created special planets for each theme for the game. After that, I listed out smaller elements associated with each theme, and highlighted the ideas I liked and color coded the ones I think can work together.
The next step I did was reorganizing and grouping all the elements I believed worked well together to flesh out game ideas. In the end I came up with 5 exciting combinations that I'm really happy with:
1st Combination - The Space Bomber
Elements: Explosion/Bombs + Buttons + Throwing + Aliens/Space + Force + Time
High Concept: After placing bombs in an alien planet, the assassin must escape to a distant aircraft before the bomb explodes. by using the force of small safe bombs, the assassin pushes himself through space to reach the aircraft in zero-gravity!
2nd Combination - Spacer Diggers
Elements: Dog + Family + Cat/Hawk + Rabbit + Test + Digging
High Concept: To train animals as assassins, humans conducted an experiment in space to train them secretly in harsh environments. Not happy with their predicament, the animals must team up together to dispatch the humans and dig their way out of the facility!
3rd Combination - Ghost Escape!
Elements: Superheroes + Clouds + Go Through Walls + Ghosts + Magnet
High Concept: The assassin must run away from superheroes after achieving his deeds using his ability to become transparent and float. But because he can't touch anything after using his powers, the assassin needs to use his trusty magnet to help him remove obstacles or fight in his favor.
4th Combination - Death
Elements: Shooting/Cutting + Cutting Shapes + Red + The Force + Tech/War + Monster
High Concept: This is the story of how a lost spirit learned how to cut though the universe to make his own weapons to kill his competitors and become death.
5th Combination - Lock & Pens
Elements: Tom Cruise + Open Locks + Stalker + Pencil/Pen + Wheels/Gears + Lock/Keys
High Concept: The pen assassin tries to escape as stealthy as possible after killing his victim with his trusty pen. When he reaches the gate, he must inject the lock with a magical liquid from his pen to open the mechanisms in order to leave.
From this experience, I learned that this is a productive approach to come up with multiple idea variations for a set theme. It's also possible to come up with branching themes that could be logged as potential future projects. Furthermore, once the ideas are constructed, it's usually easier to flesh out the mechanics, gameplay and story in reference to the elements picked.
I recommend using this method during the start on pre-production, especially if you are in a bind of constructing an idea to work on. It's an easy way to keep yourself organized and show some visualization to what you are looking for. You can also be creative with the process which also helps with the end goal! Give it a try, and happy creating!