We study the coupled $LambdaLambda nn-Xi^- pnn$ system to check whether the inclusion of channel coupling is able to bind the $LambdaLambda nn$ system. We use a separable potential three-body model of the coupled $LambdaLambda nn - Xi^- pnn$ system as well as a variational four-body calculation with realistic interactions. Our results exclude the possibility of a $LambdaLambda nn$ bound state by a large margin. However, we have found a $Xi^- t$ quasibound state above the $LambdaLambda nn$ threshold.