An antenna has an impedance on any frequency that can be measured and a way can be found to match that impedance on that band. However the impedance may be very high and/or very reactive, which can be difficult to match to with a 50 ohm radio. The high SWR increases feedline losses in particular on the higher frequency bands, but that is not the biggest issue. To some extent the usability of an antenna on another frequency depends on what losses you are prepared to tolerate and what impedances your ATU can deal with. They all have their limits. The impedance seen at the tx end of the feedline also depends on the RF length of the feedline, which is frequency dependent. Some lengths are better than others, in that the impedance seen at the tx end is more readily matched with a tuner, or in rare cases, the perfect impedance of the antenna is replicated at the tx end due to using a multiple of half wave line lengths.
As a 10 MHz dipole is also resonant on about 31 MHz, an added short wire on each end makes it a usable antenna on 28.5 MHz with some odd lobes but slightly better in two directions than a plain 10m dipole. Similarly the 7 MHz dipole is resonant on 22 MHz and requires an extra bit of wire to bring it to resonance in the 21 MHz band. you might even find that the same extension wires could be used for both adjustments. For 18 MHz, the 14 Mhz dipole is a bit long and the impedance is quite highly reactive, but your ATU might be able to deal with the impedance. For 24 MHz, again the 7 MHz dipole being resonant on about 22 is near but still reactive, so depending on your ATU and the length of your feedline you may be able to use that on 24 MHz. It will be an experimental process and no single simple solution is likely, imho.
I built my own linked dipole with links to make it work well on all HF bands. I made 10m extensions to increase its overall length to 40m for use on the 80m band. No ATU is necessary but you do have to drop the pole to adjust the links when changing bands, and I think that is the major but only disadvantage of the linked dipole.
Alternatives: I looked into this a while back and concluded that the ZS6BKW multiband dipole (an improved G5RV in some ways) when used with the designed feedline and ATU is probably a really good way to go. ZS6BKW researched the range of impedances for various antenna lengths and came up with the dipole and feedline length that gave the best compromise. Those who use them either at home or for SOTA on hilltops have great results and that is the proof of the design.