Computing inter-domain MultiProtocol Label Switching Traffic Engineering Label Switched Path (MPLS-TE LSP) using the Path Computation Element (PCE) through a predetermined sequence of domains is quite straight. Each PCE, using the Backward Recursive PCE-based Computation (BRPC), knows who is the next to be contacted in order to continue the computation. The optimality of the inter-domain MPLS-TE LSP path depends strongly on the choice of the predetermined sequence of domains on which the calculation works. In this paper we propose a novel procedure allowing a forward discovery of multiple inter-domain sequences and the computation of constrained inter-domain paths for MPLS-TE LSPs over these domains sequences. Other issues around the inter-domain path computation, such as route discovery and inter-domain loop avoidance, are investigated. Experimental evaluation shows that our solution is effective in terms of protocol and algorithmic efficiency and provides satisfiable performance with high success rate, reasonable message overhead and runtime.