If you keep the objective of the company as investing, then like @TAXIQ.IN mentioned, it won’t get approved. But you can keep your objective broad. There is no restriction on any company to invest or trade F&O in the market. For example if you are a software company, you can still trade F&O or invest in stocks both public/private.
But here is what you shouldn’t do, go actively scout for funds - telling people they can become partners in your LLP and you will manage money with them. This will be a violation of the collective investment scheme guideline by SEBI. You can check out the SEBI order on HBJ capital from few years back, where SEBI banned them from capital markets. One of the reason cited was that they were using this LLP route to manage money for people. The only way to manage money today legally is as PMS, Mutual fund/AMC, and AIF (hedge fund).