Summary: A list \({\Lambda} = \{\lambda_1, \lambda_2, \ldots, \lambda_n \}\) of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. The list \({\Lambda}\) is said to be universally realizable \((\mathcal{UR})\) if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by \({\Lambda}\). It is well known that an \(n \times n\) nonnegative matrix \(A\) is co-spectral to a nonnegative matrix \(B\) with constant row sums. In this paper, we extend the co-spectrality between \(A\) and \(B\) to a similarity between \(A\) and \(B\), when the Perron eigenvalue is simple. We also show that if \(\varepsilon \geq 0\) and \({\Lambda} = \{\lambda_1, \lambda_2, \ldots, \lambda_n \}\) is \(\mathcal{UR}\), then \(\{\lambda_1 + \varepsilon, \lambda_2, \ldots, \lambda_n \}\) is also \(\mathcal{UR}\). We give counter-examples for the cases: \({\Lambda} = \{\lambda_1, \lambda_2, \ldots, \lambda_n \}\) is \(\mathcal{UR}\) implies \(\{\lambda_1 + \varepsilon, \lambda_2 - \varepsilon, \lambda_3, \ldots, \lambda_n \}\) is \(\mathcal{UR}\), and \({\Lambda}_1, {\Lambda}_2\) are \(\mathcal{UR}\) implies \({\Lambda}_1 \cup {\Lambda}_2\) is \(\mathcal{UR}\).