Dealing with the curse of dimensionality is a key challenge in high-dimensional data visualization. We present SeekAView to address three main gaps in the existing research literature. First, automated methods like dimensionality reduction or clustering suffer from a lack of transparency in letting analysts interact with their outputs in real-time to suit their exploration strategies. The results often suffer from a lack of interpretability, especially for domain experts not trained in statistics and machine learning. Second, exploratory visualization techniques like scatter plots or parallel coordinates suffer from a lack of visual scalability: it is difficult to present a coherent overview of interesting combinations of dimensions. Third, the existing techniques do not provide a flexible workflow that allows for multiple perspectives into the analysis process by automatically detecting and suggesting potentially interesting subspaces. In SeekAView we address these issues using suggestion based visual exploration of interesting patterns for building and refining multidimensional subspaces. Compared to the state-of-the-art in subspace search and visualization methods, we achieve higher transparency in showing not only the results of the algorithms, but also interesting dimensions calibrated against different metrics. We integrate a visually scalable design space with an iterative workflow guiding the analysts by choosing the starting points and letting them slice and dice through the data to find interesting subspaces and detect correlations, clusters, and outliers. We present two usage scenarios for demonstrating how SeekAView can be applied in real-world data analysis scenarios.