This is often called a rotary group or line hunting. The telco gives you as many analogue lines as you need , and each one has an individual number to call it directly. They will also configure the first line as the pilot number, so if this first number is busy, the exchange will automatically roll over to the next number in the group.
As you suggested, this allows you to publish one number (sometimes called the LDN or listed directory number), but it will give your callers access to all of the lines.
The telcos should be able offer various hunting schemes such as circular, where the calls cycle through all lines; terminal, where calls always start at the next line and work downwards through the group, and random, where the exchange sends calls on any line in a random fashion.
