Yes. A venture capital fund is generally held in an LLC managed by a separate corporation as the management firm, the venture capital firm interacting with entrepreneurs.
A venture capital firm can consist of one person, while the LLC (the fund) can be controlled by both the management firm and the limited partners in the fund, depending on their choosing.
This is a perfect setup for a venture firm to manage multiple funds from within the same management construct, albeit it can also choose to divide the management firm up (on a general partner basis) specific to the fund at play.
Some Silicon Valley venture firms use such constructs to run sideline funds that are not venture funds at all (PIPEs and Private Equity) — making it even more fuzzy to entrepreneurs as to who has the real wherewithal to invest in venture.
I prefer the one-person, single-fund structure for the sake of establishing a real meritocracy entrepreneurs will be able to count on.