Cross-market suggestion is a technique used by social media, e-commerce platforms, and other online platforms to suggest to users' goods or services from several markets or domains. However, user engagement data (clicks, sales, and reviews) with products reveals various biases specific to certain markets, making recommendations more difficult. On the other hand, the lack of data in other markets can make it challenging to train models. Recently, the FOREC model that applies market adaptation has shown good performance on cross market recommendation problem. In this paper we propose a combined framework that employs the Light Graph Convolution Network (LGCN) algorithm, which has both market-agnostic and marketspecific models in learning cycle like FOREC but has a less complex architecture than it. The experimental results reveal that our two-stage strategy outperforms FOREC's all findings with improvements ranging from 5 to 8 percentage points with the help of an enhanced 1 to 2 percent of the market-agnostic phase in terms of nDCG@10 evaluation.