Donjr, almost any true fullrange "single driver" system is going to need a supertweeter and subwoofer(s), making it a 3-way system, in reality.
But, some have done a great job to moving the crossover between highs and lows way beyond the entire midrange frequencies.
A great starter system for a real taste of true fullrange glory is the $650
Hammer Dynamics Super-12 kit. It uses a professional 12" widerange driver to cover everything up to ~8-10kHz where it crosses over to a coaxially-mounted supertweeter.
This speaker does bass in a BIG way, along with all the benefits of other single drivers. A 12" driver has it's own benefits compared to smaller ones. There are a ton of upgrades that can be done to the speaker, like a better tweeter and crossover mods.
The kit is easily built by anyone with a table saw or circular saw and a few other simple tools. It can be made in a few hours from three or four 4'x8' pieces of plywood/mdf, if you are the least bit handy.
There are a few magazine reviews of the Super-12 on their website.