I tried to google but all I can find is NAV associated with Mutual Funds only.
Well that's essentially what you're creating so that research may be completely appropriate.
You will need to separate out your performance tracking (your XIRR sheet) from ownership. In a mutual fund, the performance of individual investments is not tracked separately - everyone shares in the overall performance of the fund equally. If the fund overall goes up 10%, everyone's investment goes up 10%.
If that is not your intent, then everyone's contributions and investments need to be tracked completely separately, and it may be best to create separate brokerage accounts for each investor.
Say your fund is currently worth $10,000 (the NAV) and a family member wants to "invest" $5,000 with you. The fund is now worth (has a NAV of) $15,000. They now own 5,000/15,000 or 33.3% of the fund. You own the remaining 2/3 (which is still $10k).
Now the next question is: what do you do with the $5,000? That's an independent decision that you must make. Do you just scale up what you're already doing? You don't even need to invest the $5,000 separately - it is now intermixed with the rest of the funds and all profits/losses are shared proportionally. If you buy a bad stock with that $5k and it goes bust, the entire fund lost $5k but each owner only loses their portion of it. They still own 1/3 of the fund.
The family member should not care about the intricacies of your XIRR calculation. All they care about is how much their $5,000 grows. They may care about what you invested in (i.e. do you have an investing strategy that you follow with all funds?) but the minutia of how each stock performs is largely irrelevant. You care about it to see how your individual choices have performed, but they just care about the size of the pot.
Now suppose the total value of investments in the fund grows to $24,000? They still own 1/3 of the fund, or $8k. It does not matter how "their" $5k performed, it is all one big shared pot.
If another family member wants to invest, repeat. They get a proportional ownership and share all profits/losses proportionally.
When someone decides to sell, then you need to make a decision on how to get them their money. Unless you have enough excess cash, you will need to decide what investments to sell. Again, you don't necessarily have to sell what you bought with their money, it's all one big pot, and they will largely be indifferent to what you actually sell.
I am not addressing the legal, tax, and relational aspects of all of this, just dealing with the mathematics of a shared investment fund.