In my opinion, I wouldn't worry too much about learning the forms of another martial art unless you're cross-training in that martial art. How forms work varies from art to art, or from style to style. I'm not just talking about simple things like how "shoulder width" in a front stance may be defined as the outside of your feet line up with the inside of your shoulders in one style, but the inside of your feet line up with the outside of your shoulder in another style.
What I'm talking about is this: some schools (which has been my experience with Taekwondo) teach the forms as rote memorized choreographed items with specific details that you must follow, and the training is largely on the attention-to-detail of copying the form the way the Master does it. It's about building repetitions with specific movements to build balance, coordination, and quick-twitch muscle (among other things). But in this context it doesn't really teach you the strategy or technique as you would fight.
Other martial arts have forms that are trained relatively similar to those in my TKD experience, but the forms are then used for bunkai (to use the Japanese term) to help apply the techniques. Where in my TKD experience, the self-defense taught at a given belt level has nothing to do with the forms, in many other styles of similar martial arts (TKD, TSD, Karate, etc.) there is a direct connection.
For example, in a school I recently attended, yellow belts learn Taegeuks 1-2. Advanced yellow belts (who are learning Taegeuk 2) have self-defense that includes knife-hand blocks, but those blocks aren't in the forms until Taegeuk 3. Other styles will take the movements in a form and use those in that portion of the curriculum in application. A simple example would be knife-hand blocks showing up in self-defense in a similar spot as the block in Taegeuk 3. A more advanced description would be to find different scissor motions for a "scissor block" with any motion where the arms cross. It may be setting up an armlock, it may be pulling their hand down to open up a backfist, it may be pulling their guard up to set up a single leg.
I believe there are also styles where the techniques are taught first and then combined into forms specifically for the purpose of having solo drills.
If your goal is to learn more forms just for performance sake, then I think you're fine learning more forms as long as it doesn't negatively affect your performance in your primary art. If you want to learn Karate kata to learn them the way Karatekas do, then I would train Karate at a Karate dojo so you can experience the full depth of that curriculum.
