The answer to that question can be summed up with one word: No. However, there are a lot of factors to consider.
This context is what defines the recommendation that you do not pitch those venture capital firms that have already invested in a direct competitor.
Here are a few reasons why you should look elsewhere for funding or further explore whether or not there might be some opportunity to work together.
It is a conflict of interest for the VC and they have a fiduciary responsibility to the company they have already invested in as well as the rest of the VC firm if there is direct competition. If they already have a company in their portfolio that does exactly what you do in terms of a product or service solution, then how can they provide strategic advice to one firm but not the same to the other?
While not every VC may have bylaws or a philosophy that firmly states it is not possible, in general, it is just not good business practice. In this case, the VC will actually let you know they cannot help due to this conflict of interest. However, they may be able to point you in the right direction of a VC that could help you.
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It is a waste of time and money for everyone involved. The VC would be working against themselves and those firms they are investing in. There is no benefit for them, you, or your competition they already have funded. Since very few start-ups actually succeed, you would want to make sure that the VC was completely focused on you, rather than trying to decide how to split their resources across the same product or solution.
Even if you decided to try anyways, the VC is most likely going to turn you down before you even get to the pitch so focus your energy somewhere else. After all, there are plenty more funding avenues out there to explore for your particular industry and business idea.
The VC is likely going to feel pulled in two different directions. It can be akin to the parent with two kids both vying for attention or looking for the parent to pick their preference over their sibling. You do not want to be in competition with another company for attention and further funding. Plus, you do not want to be in a position where the VC might share your information with your competitor.
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There is always the chance that your business plan may end up in the competitor's hands if you are working with the same investor. That can be a good or bad thing. On the good side, your competition may decide to adjust their direction and pivot away from what they see you doing, which would lessen the competitive pressure.
However, on the bad side, they may try to copy what you are doing and beat you to it. You need to consider just how private and sensitive your plan and ideas are compared to the assistance you may receive from an investor that already believes and plays in your industry.
Just remember, the same industry doesn't necessarily mean they are a direct competitor. For example, if your product or solution simply fits within a similar space or vertical as the VC’s other investments, you will definitely want to pitch that venture capital firm. Half the battle in pitching has already been won. You want to be unique and stand out within a VC’s portfolio to get the time and attention your start-up deserves.
Additionally, the VC will most likely have a track record of interest, knowledge, experience, and hopefully, success in that segment and is looking to enhance its portfolio in that arena through complementary products and services. They will also already have contacts in that segment, including potential customers, talent, and media, saving additional resources and maximizing the funding opportunity.
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There are hundreds of thousands of investors across VCs, angel investors, incubators, accelerators and crowd funders. Most likely, there are quite a few VCs out there who might be interested in your product or service, so you do not need to focus on one that already has one of your competitors in their stable. Just be sure to do your research and find a VC who is relatively close to your business, works within your sector, and aligns with your business stage, preference for involvement, and terms.