Yes, you can certainly mix and match block sizes. It gives interest to the quilt design. For example, if you have a finished 12 inch block, you can use 6 inch, 3 inch, or 4 inch blocks to make another 12 inch finished block. You can use rectangle blocks and half stagger the design when putting the blocks.
You want to use a common number to the block sizes. This makes it easier in the final layout. Next example, if you have a 10 inch block use 5, 10, or 15 inches to make the joining blocks.
You can also stagger sashing strips. One time put them on top of the block. Next block, put them on the bottom. These will still match up to needed block size but add interest too. Draw it out on paper first. Good luck with your design.