  We use two families of parameters $\{(\epsilon_{x_j},
\epsilon_{t_j})\,|\,\epsilon_{x_j,t_j}=\pm1,\, j=1,2,...,n\}$ to first
introduce a unified novel two-family-parameter system (simply called ${\mathcal
Q}^{(n)}_{\epsilon_{x_{\vec{n}}},\epsilon_{t_{\vec{n}}}}$ system), connecting
integrable local, nonlocal, novel mixed-local-nonlocal, and other nonlocal
vector nonlinear Schr\"odinger (VNLS) equations. The ${\mathcal
Q}^{(n)}_{\epsilon_{x_{\vec{n}}}, \epsilon_{t_{\vec{n}}}}$ system with
$(\epsilon_{x_j}, \epsilon_{t_j})=(\pm 1, 1),\, j=1,2,...,n$ is shown to
possess Lax pairs and infinite number of conservation laws. Moreover, we also
analyze the ${\mathcal PT}$ symmetry of the Hamiltonians with self-induced
potentials. The multi-linear forms and some symmetry reductions are also
studied. In fact, the used two families of parameters can also be extended to
the general case $\{(\epsilon_{x_j}, \epsilon_{t_j}) | \epsilon_{x_j} =
e^{i\theta_{x_j}}, \epsilon_{t_j} = e^{i\theta_{t_j}},\, \theta_{x_j},
\theta_{t_j}\in [0, 2\pi),\, j=1,2,...,n\}$ to generate more types of nonlinear
equations. The two-family-parameter idea used in this paper can also be applied
to other local nonlinear evolution equations such that novel integrable and
non-integrable nonlocal and mixed-local-nonlocal systems can also be found.
