diff --git a/src/multivariate/mvnormal.jl b/src/multivariate/mvnormal.jl
index 6126c1d8f1..0c9bab9e25 100644
--- a/src/multivariate/mvnormal.jl
+++ b/src/multivariate/mvnormal.jl
@@ -166,13 +166,20 @@ Generally, users don't have to worry about these internal details.
 We provide a common constructor `MvNormal`, which will construct a distribution of
 appropriate type depending on the input arguments.
 """
-struct MvNormal{T<:Real,Cov<:AbstractPDMat,Mean<:AbstractVector} <: AbstractMvNormal
+struct MvNormal{T<:Real,Cov<:AbstractPDMat{T},Mean<:AbstractVector{T}} <: AbstractMvNormal
     μ::Mean
     Σ::Cov
+
+    function MvNormal{T,Cov,Mean}(µ, Σ) where {T<:Real,Cov<:AbstractPDMat{T},Mean<:AbstractVector{T}}
+        axes(Σ, 1) == eachindex(μ) || throw(DimensionMismatch("The dimensions of µ and Σ are inconsistent."))
+        T(Inf)     # we require that Inf be in the domain of T, see `insupport`
+        return new{T,Cov,Mean}(µ, Σ)
+    end
 end
 
 const MultivariateNormal = MvNormal  # for the purpose of backward compatibility
 
+# TODO?: make these IsoNormal{T} etc
 const IsoNormal  = MvNormal{Float64,ScalMat{Float64},Vector{Float64}}
 const DiagNormal = MvNormal{Float64,PDiagMat{Float64,Vector{Float64}},Vector{Float64}}
 const FullNormal = MvNormal{Float64,PDMat{Float64,Matrix{Float64}},Vector{Float64}}
@@ -182,32 +189,49 @@ const ZeroMeanDiagNormal{Axes} = MvNormal{Float64,PDiagMat{Float64,Vector{Float6
 const ZeroMeanFullNormal{Axes} = MvNormal{Float64,PDMat{Float64,Matrix{Float64}},Zeros{Float64,1,Axes}}
 
 ### Construction
-function MvNormal(μ::AbstractVector{T}, Σ::AbstractPDMat{T}) where {T<:Real}
-    size(Σ, 1) == length(μ) || throw(DimensionMismatch("The dimensions of mu and Sigma are inconsistent."))
-    MvNormal{T,typeof(Σ), typeof(μ)}(μ, Σ)
+## Constructor that accepts an `AbstractPDMat` but coerces only T and Cov
+function MvNormal{T,Cov}(μ, Σ::AbstractPDMat) where {T<:Real,Cov<:AbstractPDMat{T}}
+    # General pattern: `convert(Typ, x)::Typ` is used to coerce `x` to type `Typ`
+    # This guards against broken implementations of `convert` that otherwise risk StackOverflowError
+    μ = convert(AbstractVector{T}, μ)::AbstractVector{T}
+    return MvNormal{T,Cov,typeof(μ)}(μ, Σ)
 end
 
-function MvNormal(μ::AbstractVector{<:Real}, Σ::AbstractPDMat{<:Real})
-    R = Base.promote_eltype(μ, Σ)
-    MvNormal(convert(AbstractArray{R}, μ), convert(AbstractArray{R}, Σ))
+## Constructor that accepts an `AbstractPDMat` but coerces only T
+function MvNormal{T}(μ, Σ::AbstractPDMat) where {T<:Real}
+    Σ = convert(AbstractPDMat{T}, Σ)::AbstractPDMat{T}
+    return MvNormal{T,typeof(Σ)}(μ, Σ)
 end
 
+## Constructor that accepts an `AbstractPDMat` without any coercion
+function MvNormal(μ, Σ::AbstractPDMat)
+    T = promote_type(eltype(μ), eltype(Σ))
+    return MvNormal{T}(μ, Σ)
+end
+
+## Coercing constructors that accept a general covariance matrix
+MvNormal{T,Cov}(μ, Σ::AbstractMatrix) where {T<:Real,Cov<:AbstractPDMat{T}} =
+    MvNormal{T,Cov}(μ, Cov(Σ))
+MvNormal{T,Cov}(μ, Σ::UniformScaling) where {T<:Real,Cov<:AbstractPDMat{T}} =
+    MvNormal{T,Cov}(μ, pdmat(T, length(μ), Σ))
+MvNormal{T}(μ, Σ::AbstractMatrix) where {T<:Real} = MvNormal{T}(μ, pdmat(T, Σ))
+MvNormal{T}(μ, Σ::UniformScaling) where {T<:Real} = MvNormal{T}(μ, pdmat(T, length(μ), Σ))
+
 # constructor with general covariance matrix
 """
     MvNormal(μ::AbstractVector{<:Real}, Σ::AbstractMatrix{<:Real})
 
 Construct a multivariate normal distribution with mean `μ` and covariance matrix `Σ`.
 """
-MvNormal(μ::AbstractVector{<:Real}, Σ::AbstractMatrix{<:Real}) = MvNormal(μ, PDMat(Σ))
-MvNormal(μ::AbstractVector{<:Real}, Σ::Diagonal{<:Real}) = MvNormal(μ, PDiagMat(Σ.diag))
-MvNormal(μ::AbstractVector{<:Real}, Σ::Union{Symmetric{<:Real,<:Diagonal{<:Real}},Hermitian{<:Real,<:Diagonal{<:Real}}}) = MvNormal(μ, PDiagMat(Σ.data.diag))
-MvNormal(μ::AbstractVector{<:Real}, Σ::UniformScaling{<:Real}) =
-    MvNormal(μ, ScalMat(length(μ), Σ.λ))
-function MvNormal(
-    μ::AbstractVector{<:Real}, Σ::Diagonal{<:Real,<:FillArrays.AbstractFill{<:Real,1}}
-)
-    return MvNormal(μ, ScalMat(size(Σ, 1), FillArrays.getindex_value(Σ.diag)))
-end
+MvNormal(μ, Σ::AbstractMatrix) = MvNormal{promote_type(eltype(μ), eltype(Σ))}(μ, Σ)
+MvNormal(μ, Σ::UniformScaling) = MvNormal{promote_type(eltype(μ), eltype(Σ))}(μ, Σ)
+
+pdmat(::Type{T}, Σ::AbstractMatrix{<:Real}) where {T<:Real} = PDMat{T}(Σ)
+pdmat(::Type{T}, Σ::Diagonal{<:Real}) where {T<:Real} = PDiagMat{T}(Σ.diag)
+pdmat(::Type{T}, Σ::Union{Symmetric{<:Real,<:Diagonal{<:Real}},Hermitian{<:Real,<:Diagonal{<:Real}}}) where {T<:Real} = PDiagMat{T}(Σ.data.diag)
+pdmat(::Type{T}, n::Integer, Σ::UniformScaling{<:Real}) where {T<:Real} = ScalMat{T}(n, Σ.λ)
+pdmat(::Type{T}, Σ::Diagonal{<:Real,<:FillArrays.AbstractFill{<:Real,1}}) where {T<:Real} =
+    ScalMat{T}(size(Σ, 1), FillArrays.getindex_value(Σ.diag))
 
 # constructor without mean vector
 """