Mid Arm machine with feed dogs?
 

Is there such a thing as a mid arm machine that you can use to piece the quilt? I don't have room for a regular mid arm that is only for free motion, but would love one that would do both. Thanks.

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.

You could look at the Brother pq 1500sl or Juki 2010q

I have a Brother 2400 with an 11.25" throat, but would love a 15" regular machine. SIgh. Maybe one day, the manufacturers will come out with one.

Please reference my note above ............. TBH while 15" seems huge in comparison, when doing FMQing, it really is not.
...... Been there, done that and have the t-shirt! :D

Look at the Babylock Jazz it has a 12" throat.

The Janome M7Continental has 13” to right of needle and is set up for super good visibility around the needle. You might want to take a look at it if there’s a dealer nearby.

Rob