This is a follow-up question to https://puzzling.stackexchange.com/q/41241/29343.

Consider a 7x7 grid of math operators `o` and numbers `A, B, ..., P`:

    A o B o C o D
    o o o   o o o
    E o F o G o H
    o   o o o   o
    I o J o K o L
    o o o   o o o
    M o N o O o P

This grid encodes 10 math equations. There are 4 horizontal equations, 4 vertical, and 2 diagonal. Specifically:

    A o B o C o D
    E o F o G o H
    I o J o K o L
    M o N o O o P
    A o E o I o M
    B o F o J o N
    C o G o K o O
    D o H o L o P
    A o F o K o P
    D o G o J o M

Note that the central operator `o` at position (4,4) is shared by *both* of the diagonal equations.

The question is: **Can the letters `A` through `P` be replaced with all distinct numbers `1` through `16` in any order, and the placeholder operators `o` by `+` or `*` or `=` such that all 10 grid equations are satisfied?** Operator precedence is the usual, no grouping is allowed.

Are there lots of solutions or none at all?