Chaining overloaded operators with different parameter types

Let's say I have a class "Vector" (Math not Container) and I'd like to overload the operators, so I can chain calculations.

That works fine for me:

friend Vector operator+(const Vector<N, Type>& a, const Vector<N, Type>& b)
friend Vector operator+(      Vector<N, Type>& a, const Vector<N, Type>& b)

and with that I can do stuff like

auto a = vec<3>(.0f, .0f, .0f);
auto b = a + a + a;

However I also implemented an initializer list

Vector& operator=(Type const (&arr)[N])

Which makes it possible for me to write something like this:

a = { .1f, .1f, .1f };
a += { .1f, .1f, .1f };

However what I can't do is chain those initializer lists.

a = { .1f, .1f, .1f } + b;
a = { .1f, .1f, .1f } + { .1f, .1f, .1f };

I already tried adding operator overloads like

friend Vector operator+(const Vector<N, Type>& a, Type const (&arr)[N])     
friend Vector operator+(      Vector<N, Type>& a, Type const (&arr)[N])     
friend Vector operator+(Type const (&arr)[N], const Vector<N, Type>& a)     
friend Vector operator+(Type const (&arr)[N],       Vector<N, Type>& a)   

but it doesn't work...

Is this possible?