Obviously a fund is already spread across multiple markets and companies.
Your fund might be distributed across markets and companies. Other funds might not be distributed at all. Fund X might not have an international component. Fund Y might be tech heavy. Fund Z might be emerging markets.
You decide how you want to diversify your investments and then you say what funds you need to invest in to get to that point.
Now too many funds can cause you to have duplication and that can skew your diversification if you aren't paying attention. You can also have to look at minimum investment levels. So you may not be able to put money into another fund until your account gets large enough.
My initial thoughts are this will incur more management fees overall,
but provide the benefit of a more diverse portfolio (assuming you
invest in different types of funds that don't just invest in the same
things as the other fund(s))
If the fund has a flat fee for management or charges a fixed amount per transaction your costs can go up unnecessarily if you have too many funds. But if the annual if x% of the fund balance then it doesn't make a difference if you have multiple funds.
Too many funds can be harder to track, but if you are talking about going from one fund to three or four that shouldn't be a big concern.