If I were strongly inclined to use a dome midrange in a 3-way speaker, I would consider this dome by Peerless/Tymphany available through PE:
https://www.parts-express.com/Peerless-GBS-85N25PR03-04-3-1-2-Paper-Cone-Midrange-4-Ohm-264-1494
The diameter is better than it is with the more common 2" domes, but not by as much as you might think if you focus on the "3 1/2" description. The specifications from the manufacturer indicate that the "effective" dome diameter is 6.7 mm = 2.64", and this most likely includes some of the surround. However the slight improvement in diameter gives it a significant improvement in piston area, 35 cm^2 vs. 28 cm^2 for the more common 2.125" dome midrange. The linear excursion is given as 2.1 mm, twice greater than the typical 1 mm value for a 2" dome. The net effect of the advantage in piston diameter and linear excursion is that the advantage in volume displacement is 2.1 x 35/28 = 2.6. With volume displacement 2 1/2 times greater than it is with a typical 2" midrange, this dome midrange should be usable a octave lower, to perhaps 500 Hz, depending on how loud you want it to play. This is low enough in frequency that it would not be unreasonable to build a 3-way speaker using this dome midrange.
The reason for the greater linear displacement probably is more about the motor than the suspension. The coil height is not stated in the specs, but the gap height is given as 3 mm. Together with the low DCV, this suggests that the motor is probably underhung, i.e., that the coil height is probably about 1 mm, about the same as it typically is with a tweeter. Interestingly, the coil diameter is given as 25.7 mm, just barely more than 1", which obviously means that the coil former joins to the dome not at the edge of the dome but rather slightly inward from the edge of the dome. If the manufacturer's graph of frequency response is to be believed, it is extremely flat from about 150 Hz to 2 kHz. It would be interesting to see measurements of distortion for this driver, because it may well be the ideal midrange to fill the directivity gap between a 6" or 7" woofer and a typical 1" tweeter. For a woofer larger than this, I would still go with a larger midrange.
There is also a true 3" soft dome by ScanSpeak, however it seems to offer minimal advantage over the smaller domes because the linear excursion is .8 mm. It uses an overhung motor with coil height 2.9 mm and gap height 2 mm. This is a little surprising given that the coil is 3" in diameter. This suggest a somewhat high value for DCR of the coil and somewhat low efficiency and sensitivity. DCR is 5.7 ohm and sensitivity is quoted as 92 dB. However this quoted sensitivity value is very misleading because the response has a horrific peak. To be usable down to 500 Hz the peak will have to be squashed and the effective sensitivity will only be about 85 dB, not so good. The peakiness of the response will be further exacerbated by the high Q of the driver unless the enclosure for it is impossibly large, because total Q is 1.73. The same issue is encountered to a lesser extent with the Peerless dome, which is similarly open in the back, but which has Qts .63. While this is greater than is to be desired it is usable, even though it wants to be given as much volume as can be allocated to it. (Qts is greater than the maximum value at which the enclosure volume would be less than Vas for resulting system Q of .7; Vas is 1.6 liter. This suggests that in a typical application its response will likely exhibit a modest peak at the low end, however it should not be difficult to correct this in the applied high-pass filter.)
Once again the fundamental limitation of large domes becomes apparent. The large diameter of the coil implies greater mass and larger DCR, which confounds good efficiency and sensitivity. It is manifest that the motor should be underhung to avoid this fundamental drawback, but even when the coil is short, sensitivity is barely acceptable without using larger diameter for the coil wire, and larger diameter for the coil wire increases the mass, such that it ends up sort of like a dog chasing its tail so to speak. Ultimately in order to achieve a flat response to adequately high frequency it is necessary to use a coil that is both short and small in diameter, like Tymphany did with the GBS-85N25PR03-04. If I were wanting to build a 3-way speaker with a woofer not larger than 6.5", I would seriously consider using this dome midrange.
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