Your option is to get one of the larger regular-style machines with a larger throat aka greater space between the needle and post.
This will let you "stuff" more of a quilt sandwich through that opening, but it is not as free and open as the sit-down Sweet-16 style machines.
All that being said ... do a cost analysis ... if your regular stitching machine is doing what you want it to do, other than the FMQing, you may find that purchasing a S-16 type may cost you less than purchasing the larger throated machine and still be faced with the limitations a traditional styled machine presents.