Easy orthogonalization against other MulQuasiVectors

Sometimes, I need to orthogonalize a MulQuasiVector against a set of
other MulQuasiVectors:

Currently, I do it like this:

const RadialOrbital{T,B<:AbstractQuasiMatrix} = MulQuasiArray{T,1,<:Mul{<:Tuple,<:Tuple{<:B,<:AbstractVector}}}

struct Projector{ΦT,B<:AbstractQuasiMatrix,RO<:RadialOrbital{ΦT,B}}
    ϕs::Vector{RO}
end

projectout!(y::RO, ::Nothing) where RO = y

function projectout!(y::RO, projector::Proj) where {RO,Proj<:Projector}
    yc = y.mul.factors[2]

    for ϕ in projector.ϕs
        c = ϕ'y
        yc .-= c*ϕ.mul.factors[2]
        # y -= c*ϕ # It would be nice if this worked
    end
    y
end

Could we get y -= c*ϕ syntax working? It would be nice if that did not have to be implemented for every kind of basis, but just in ContinuumArrays.

Start by tracing the existing MulQuasiArray and MulQuasiVector operations used by the Projector example, especially scalar multiplication and subtraction. Reproduce the orthogonalization snippet and investigate whether y -= c*ϕ can use the general ContinuumArrays abstractions. Done means the syntax works for the shown MulQuasiVectors without basis-specific implementations.