Need help with wiring second pair of speakers

I am considering hooking up a second pair of speakers to my 2 channel system. My integrated amp has only one set of left and right speaker terminals. I have heard that improper wiring can cause serious impedence issues.  My amp puts out a good amount of power. My primary pair of speakers are rated at 6 ohms (nominal) and the second pair are rated at 4 ohms (nominal). 

My questions are:
Firstly, will the two different impedences be compatible?
Secondly,  do I wire them parallel with cables from the amp feeding both sets of speakers; or in series by hooking up the second pair from the first pair?  I know one of these is wrong, but not which one.

The difference in impedance doesn’t matter, what does is your amp 2ohm stable? Being an integrated amp it’s unlikely, so connecting them in parallel would most likely smoke the amp. Connecting them in series your amp will see 10 ohms so no worries, but what’s the point. Connecting them this way will reduce the amps output with no resulting increase in volume. And the difference in impedance would most likely see one pair much louder than the other, depending on sensitivity of course.

My question is, does your amp have pre outs and a set of main inputs? If so, purchase a power amp, connect it to the integrated with some Y adapters, this way you can drive both sets. The only caveat would be, look for an amp with adjustable gain so you can balance the speaker outputs if in the same room.

Impedance for 4 ohm and 6 ohm in parallel is 2.4 ohms, in series is 10 ohms.

A series connection is + from the amp to + of the first speaker, then - from first speaker to + of the second speaker, and - of second speaker to - on the amp. A parallel connection can be a separate cables to each speaker from the amp or connecting second speaker directly to the first. Both of your descriptions seem to imply parallel.

Series is the safest, but will likely not sound good, and parallel will likely be too low of an impedance load for the amp.

Is this second pair of speakers for the same or different room?

Thanks for the clarity. The second speakers would be in the same room. The idea is to balance the voice of the first set, which are what some call "bright" or "analytical", with the second set that are "laid back" or "mellow". I'm thinking that a blend of the two might cover all bases and smooth out the bright speakers without loosing the crispness and sparkle.
The second speakers would be in the same room. The idea is to balance the voice of the first set, which are what some call "bright" or "analytical", with the second set that are "laid back" or "mellow".
I would not recommend that kind of approach, even apart from the impedance and sensitivity issues that have been cited. What will happen is that the sounds from the two sets of speakers will not arrive at your ears at precisely the same time, resulting in what are called comb filtering effects. Which will most likely result in a significant loss in clarity, and a general "cloudiness" to the sound.

Also, a further point about series connection, which was properly defined in the post by Tony (Tls49): If speakers that are different models are connected in series the differences in how their impedances vary as a function of frequency are likely to result in significant frequency response irregularities in both speakers. The reason being that the voltage applied by the amplifier to the series-connected speakers will divide up between the two speakers differently at different frequencies.

And regarding parallel connection, keep in mind that the 2.4 ohm combined impedance of the two speakers is based on their **nominal** impedances of 4 and 6 ohms, and is likely to be even less than that at some frequencies.

-- Al

if you need both for lets say a seprate room you could find a quality speaker selector that will impedence match so the load is not so low for your amp but you will lose a little sound quality that way. its what amps do with two speaker conections internaly if you had an integrated amp with more then one hook up. if your using them in the same room i would look at the above posts as its not really recomended as you really dont gain anything and the losses are to great.
Yes, Niles makes speaker selectors that also incorporate volume controls to balance the speakers. But as mentioned, they are really intended for whole house setups with ceiling or wall mount speakers where critical listening isn't the goal. I've used them in the past for custom installations for customers, but never for personal use so no real long exposure experience. I don't know, but it just might be the ticket for your needs.

Heres a link to a picture of the Niles unit. They also have models for more extensive systems, plus units that only switch between pairs without gain controls.

Y'all have convinced me that I had an ill conceived idea. Thank you for saving me the time and trouble of trial and error.
Not necessarily a bad idea, running two pair of speakers stacked has its aficionados. Often owners of the large Advents are bent on doing this and swear by it. Had never attempted something like this so having two pair of series I Klipsch Heresys around the house and the little lady wasn't here it got me thinking.

Dragged the other pair out into the living rm and had at it. Dynamics out the ....... but the overall sound just wasn’t the direction I was going.

Attached is a pic with the stacked Heresys lol.

From the picture, looks like I had just received the Rock and a couple of Kenwood KA-4006 integrated amps and setup for testing.