Which to Upgrade first? My Amplifier or Speakers?

Norman, honestly, what do you listen to? Speakers or associated equipment upstream?
Get your speakers straight, then all of your sources (most of which are todays technology) will fall into place.

OK question for OP. You posted this on the pro section so are you interested in a rehash of all the homeowner stuff talked about so far or are you really interested in pro gear?
  Pro gear opens your world to astounding speakers from Klipsch. The K-402 horn lens is the best in the world right now and you can mate it with various bass bins either direct radiator or horn type.
  Currently I run a home build Super MWM bass bin which is a variant of the Klipsch MWM bin except mine goes down to 27hz as a single fold horn. On top is a K-402 horn with the 1132 driver and run it off a pair of Crown xli800's and a Xilica DSP. You can build an astounding system like this for about $6,000 and that is with new K-402 horns as your chance of finding used is about zero.
  If you are not into building but would rather just buy, the Klipsch Jubilee is a whole lot cheaper than a ton of all this name dropper stuff and has prodigious sound. If you really want to enter into the world of genuine hi end sound you are going to have to migrate to a DSP and multiple amps. It is daunting to start off doing this but the reward is jaw dropping sound and FAR less $$$$ than most all this fru fru stuff touted around here. You can PM me if interested and I will fill you in on what I did and why.
  Just for grins though you can look up Klipsch KPT-456, MCM 1900's which were my two prior systems and I can tell you the existing Super MWM beats the MCM 1900 easily. You just have no idea the superb fidelity pro gear brings to the table and a darned sight less than all that name dropper stuff.

Upgrade your speakers first because you would never ever have sound as good as if you have great speaker door about the amp if you got Grace speakers you will be all right I know from experience.

 Hi Norm,

I hear yah .... I'm not knocking your system, you have some fine equipment there, on paper, but it's not paper we listen to.

I'm with Erik Squires and Optimize, the room is an extension of your system, but perhaps you've already addressed that, if not, start there. You may also consider running a designated circuit with appropriate grade wire from your panel (12 AWG) into good quality plugs.

 

I like the Maggie's - - - but not that much. They seem to be paired with Mac gear a lot (at Hi-Fi shows and retailers). One thing I'll say for Mac gear is it's reliable, the Kalashnikova of audio. Thing is they have a similar sound as well ..... dull. I spent an afternoon at Broadway Sound in Vancouver listening to a pair of big Mac monos (model slips my mind) and a pair of 3.7 Maggie's. The Mac's were running just about flat out, and I thought - - - where's the beef. Like I said, I find Mac amps dull and uninvolving - - - but that just MHO.

 

You're in a bit of a pickle there Norm, if you're going to move up the audio latter as opposed to a lateral move you're looking at some pretty esoteric gear, which is not only pricey, but rare. Roberjerman suggested Quad 2905's, nice speaker, but Quads are like Italian cars.

 

I wish I could be more suttle, but I can't (for your sake), can the Mac gear! Go used.

Speakers: Martin Logan Quests/or Requests, $1500.00 and if you have a big room the Prodigies.

Amp: Krell KSA 300S $3000-$4000, or Threshold SA12e, or Sim Moon W10's $3000 - $4000.

Pre-Amp: C.A.T, or an Atma-Sphere MP-1 or MP-3, or Audion Premier 2 box Silver Night. On a budget, a giant killer VTL Ultimate $2000.00.
One last thing - you may solve your issues with a phono cartridge, there I would suggest a Soundsmith Aida MKII.
Good luck & happy listening.

Hi Norman,

I found myself in a similar situation, where I was very happy with my components however was searching to do better. I was getting advice to change speakers, change Amps, Pre- Amps etc. But I felt that would only result in me having a different system which would ultimately be an expensive lateral move rather than a strategic move forward.

After a lot research and some sage consulting- I found that the least expensive and most efficient path forward was to maximize my investment in the components I already had.
 
Components make up about 50/60% of your system. If you are happy with what you have, then its time to make a committed invest in the other 40/50%  of your system.

As Some have already pointed out - That would include

1. Power Delivery - Most often overlooked, however most electronics only operate at 50% capacity because they are starved for more power. More Power results in greater soundstage,  clarity, detailed imagery etc... - Stock power chords will not get you to where you want to be.

2. Addition of Subwoofers - Your  Maggie's frequency response currently is about 34Hz /29Hz (broken In) - 40kHz. A good pair of  Subs will allow you to capture a larger Sound Stage beginning at 20Hz going up to 40kHz. This would reveal a wealth of details that you are currently not experiencing in the mid range(enhanced spacial separation) as well as getting you down to a consistent low end. Those measurements are not exact, but rather reference points to guide you. More accurate measurements  would be dependent on  #3

3. Room Enhancement - Also overlooked, but very important. If you have the means, Dedicated Space and Money. Definitely worth the investment.
Something I am still working on.

If 12k Is your initial budget, I would explore #1 and #2 first. As others have pointed out - take advantage of the used market.  Then save up for #3 when you have a substantial budget to make a real difference. Also realize that you are happy with your components now so you have time on your side. Any changes you make that move you towards your goal is a Plus. Enjoy!!