Consider two bipartite graphs \(G=\{L,R,E\}\) and \(G'=\{L',R',E'\}\). A bijection \(f:L\cup R\to L'\cup R'\) such that \(f(L)=L'\) and \(f(u)f(v)\not\in E'\) for every edge \(uv\in E\) is called a bi-placement of \(G\) and \(G'\). The graphs \(G\) and \(G'\) are called bi-placeable if there exists a bi-placement of \(G\) and \(G'\). The authors present new sufficient conditions for bipartite graphs \(G\) and \(G'\) to be bi-placeable. For the case when all vertices of \(R\) and \(R'\) are isolated or pendent, the authors go on to present a necessary and sufficient condition for \(G\) and \(G'\) to be bi-placeable.