Iterative rank reduction implemented via multichannel singular spectrum analysis (MSSA) filtering has been proposed for data deblending. The original algorithm is based on the projected gradient-descent method with a projection given by the MSSA filter. Unfortunately, MSSA filters operate on data deployed on a regular grid. We have developed a way to adopt a recently proposed modification to MSSA, interpolated-MSSA, to deblend and reconstruct sources in situations in which the acquired blended data correspond to sources with arbitrary irregular-grid coordinates. In essence, we develop an iterative rank-reduction deblending method that can honor true source coordinates. In addition, we indicate how the technique also can be used for source regularization and interpolation. We compare our algorithm with traditional iterative rank reduction that adopts a regular source grid and ignores errors associated with allocating off-the-grid source coordinates to the desired output grid. Synthetic and field data examples indicate how our method can deblend and reconstruct sources simultaneously.