I own a Software Development business with just myself. I use it for all of my freelance work. I also have tons of experience with Private Investigations and I have a few old clients wanting to know if I still do PI work. My business is registered in CO so I can legally do PI work without a license. My question is, can a single business entity perform multiple different services that are not alike? Can a development company also do Private Investigations under one roof? The PI work is simply going to be a very secondary service that will only be casually advertised.
Yes - at least in my state (Maryland).
I formed an LLC in June 2012, not exactly sure what I'd be doing at the beginning. So my website promoted that I was a user experience designer and QA tester. (I never got any QA work through the business despite a previous background in it, so by the end of the year I was only a UX designer.) I've also explored the possibility of doing photography professionally on the side. Through the LLC, that is possible. However, I decided against that because of the tax situation. (I would have to sell photography equipment that I already own to my company - from me to me - and account for that in taxes.)
What I did to have effectively a general purpose LLC was this: I worded my company's statement of purpose in its Articles of Organization to effectively allow for any kind of work. It says the purpose is "... user experience consulting and to engage in any other lawful act or activity for which a Limited Liability Company may be formed in the state of Maryland."
If Colorado requires you to do a personal property return or otherwise say what equipment you use in the business, you need to tell them both the items you use for software development and the items you use for PI.
Edit: Some sources using the "any other lawful purpose" example:
State of Maryland Attorney General ("any lawful activity")
BizFilings: "When a more detailed description is used, the generic or catchall phrase 'any other lawful purpose' should be used in addition to the detailed description."
An example with Colorado: "and to pursue any other lawful purpose for which a limited liability company may be organized under Colorado law."
I have done some cursory searching, and it seems what you are proposing is "unrelated diversification". I am having a hard time finding if there is any way to have such acts be illegal. Quite the opposite, I have been finding nothing but a myriad of strategies on how to diversify. That said, I would recommend contacting a lawyer who is licensed to practice in your area for a final word. If you don't want to ask a local lawyer, you can always go to a legal website (a few of them are free) and ask there. I would highly recommend doing one or the other.