How to downscale an image with interpolation by a factor larger than interpolation kernel size?
It is arguably inefficient. You could achieve the same results with a single processing step using a single kernel. You can do this by convolving all of the kernels together, then applying your resize using this larger kernel.

A similar process to this is used in most digital painting packages. The resizing usually offers some fixed kernel sizes (e.g. bilinear / bicubic - these may be referred to as 'smoother' / 'sharper') as well as some form of intelligent resize (sometimes called 'smart' or 'best quality') where the resampling kernel size is a factor of the image size.

If you need more information you should add some details about what precisely you are trying to achieve.