Innovation is an important source of growth for many companies. It is also challenging, as it may require that the companies build a new position in the supply chain. The literature is devoid of analysis of different ways to build such positions in the construction industry. The purpose here is to explore the challenges involved in implementing innovations that require companies to establish new positions in a construction supply chain. Three in‐depth case studies in the Swedish timber housing industry illustrate different challenges that arise with the different modes of repositioning of organic growth, collaboration and acquisition, and with moving either backward or forward in the supply chain. Organic growth is a slow process that prevents companies from taking a first‐mover advantage. Acquisitions can involve difficulties with exploiting acquired competences. Collaboration brings the risks of diversity of interests and transient solutions. Furthermore, and as shown in the cases studied, challenges are associated with pre‐existing competencies and relationships, with technology‐oriented companies facing customer‐related difficulties and market‐oriented companies mainly facing ones involving technological solutions. The construction industry’s idiosyncrasies amplify these challenges, as its fragmentation makes it difficult to connect with external companies at new positions. Stronger ties with business partners are likely to enable construction companies to exploit more easily innovations that require repositioning in the supply chain.