It's a great question!
Trajectory
To get a few decades more out of them, you can launch Voyagers 3 and 4 sometime around now and get by with a maximally-boosting flyby of Jupiter since you wouldn't target Saturn as well. If you had to wait for Jupiter and Saturn to line up with the original pair's trajectories again, it would be too long of a wait.
However, without Saturn, you'll eventually fall behind again, so this is a stop-gap measure.
I recommend you ask a new question if you'd like some detailed planning for spacecraft that could chase the Voyagers for communications relay purposes. There are a lot of considerations there and the question would have to be more specifically defined.
Source
Link Budget
Let's look at the link budget.
In order to have a useful communications link, you need to receive a signal that's at least roughly the same strength as the local thermal noise of your receiver.
You calculate the ratio of the received power to the transmitted power in decibels by adding the gain of the transmitting and receiving antennas together, then subtracting the path loss. You can read more about that in this answer to the question How to calculate data rate of Voyager 1?
In order to get a bandwidth sufficient for 160 bits per second between Voyager 1 and Earth, you need a 3.66 meter dish on Voyager (48 dBi) and a 70 meter dish on Earth (~73 dBi). Even then you get about -150 dBm (-180 dBW) signal ($1 \times 10^{-18}$ Watts) and you need a liquid helium cooled receiver front-end to pick it up out of the noise.
You can read much more about Voyager communication with Earth in the DESCANSO Design and Performance Summary Series Article 4; Voyager Telecommunications
See also Why does DSN sometimes uses two dishes at the same time to receive Voyager-1?
If you wanted to double the range of Voyager 1 and 2 with Voyager 3 and 4, the second two would need 70 meter dishes that maintained sub-millimeter surface accuracy. This technology is certainly possible but it doesn't exist and would have to be developed.
According to answer(s) to What's the largest area dish antenna sent beyond the Earth-Moon system? the answer is only 4.6 meters (Galileo). For antennas deployed in cis-lunar space, see answers to What is the largest antenna deployed in space? show a few things larger, but these would not be suitable.
This kind of thing just isn't done, and it probably won't be, since optical communication is definitely the way to go in the near future. We've already had demonstrations from Earth to the Moon, and there are no known roadblocks to extending optical communications to deep space. Since the wavelength of light (about 1 micron) is so much smaller than the wavelengths used in deep space (centimeters, perhaps millimeters in the future) the "dish" shrinks from a huge steel monstrosity to the mirror of an optical telescope tens of centimeters in diameter. This can be managed quite nicely on a deep space probe.
For examples of similarly-sized optical telescopes that have already been in deep space, see answers to What's the largest aperture telescope sent beyond the Earth-Moon system?.
Once deep space optical communications is active, it may definitely be worth considering something like optical relay stations.
Not something you'd want to put in deep space!
Here is what a "steel monstrosity" looks like. This is the 70 meter dish at the Deep Space Network's Goldstone facility, there is also one in Australia and one in Spain. The red lines mark stairs and walkways, for scale.
One in space would of course be lighter, but keeping it stiff enough to produce an accurate surface figure may still make it too heavy to launch to deep space.
above: Photo credit JPMajor, creative commons CC BY-NC-SA 2.0.
above: From commons.wikimedia.org.
