There is a little more to it than you think.
First, it is important for the JFETs to be reasonably well-matched. It is important for the musicality of "the turnaround" - that point where the phaser reaches the end of the sweep and starts going back in the opposite direction. If the JFETs are not matched, you can find yourself in a position where several of them may crap out and not change resistance for the remainder of the sweep, and effectively "sit it out on the bench", waiting for the other JFETs and the sweep to come back around again. Ideally you want all the JFETs to change resistance together. Naturally, the more JFETs are involved, the harder it becomes to match them. Or rather, the more JFETs you have to buy and measure in order to find a matching set. You can certainly do it, but it won't be as easy as buying 4 more JFETs and installing them.
Second, you'll need to manage feedback very carefully. Hiss accumulates over phase-shift stages, and if that "hiss-enriched" signal is fed back to the input, it will be enhanced. So what you'll see in many phasers with more than 4 stages is a small-value cap in the feedback loop of one or more of the stages to trim some of the treble off. There is also the matter of riskingoscillation with more stages. In principle, each stage should have a gain of 1x. In practice, the 5% tolerance on resistors means that a stage here or there could have a gain as high as 1.1x. That doesn't sound like very much, but if, say, 3 out of 8 stages had a gain of 1.1x., you end up with an overall gain of 1.33x. And if you feed that back to the input, multiplying it by 1.33 yet again, you can verge into oscillation very easily if you don't cut back on resonance/Feedback. You'll also need to decide where you want the feedback tapped from and fed to. If, let's say, you insert the additional 4 stages between stages 2 and 3, that will make your feedback loop straddle 7 stages, which may not be to your sonic liking.
Even though you may figure out a way to manage the feedback, so that oscillation doesn't break out, the risk of gain in an 8-stage version (or attenuation if the 5% tolerance mean ach stage has a gain of .95x!) means that achieving a 50/50 dry/wet match for greatest notch depth will require some tweaking.
Let me emphasize that none of this is insurmountable, and it could sound fabulous. But at the same time, what you are aiming for is not as simple as just throwing another 4 stages on there. This is one of the reasons why phasers that use more than 4-6 stages tend to be noticeably more complex designs.
If you want a compromise, the simplest solution is to add a pair of fixed phase-shift stages with a dual op-amp between stages 2 and 3. It will yield an additional notch and a discriminably different sound, but without many of the issues noted above. No JFETs to match. It's a simple daughter board to make on perf/vero, and insert as an addendum to any existing 4-stager. Run V+, gnd, in and out wires between the daughter and main board, by cutting the trace between stages 2 and 3, and away you go. I've done it, and it works fine. You will note that many multi-stage phasers employ fixed stages to supplement the swept ones; the MXR Phase 100 and the Boss PH-2/RPH-10 among them.
I know I stressed the importance of having matched JFETs that continue to change resistance, and a pair of fixed phase-shift stages will obviously not sweep. The difference is that they provide a constant contribution to total phase shift, and don't simply stop sweeping before you get to the top or bottom of the sweep, as would be the case with mismatched JFETs.