3-ch amps vs. mono blocks vs. stereo amp + mono?

I am looking to add some power to my system which right now is being driven by an integra dtr 40.1. Initially I will continue to use that receiver as the processor but I want to add some power on the output side (200w or so).

I only have one system so it has to pull double duty for HT and music reproduction. So, what are the pros and cons of getting a 3-ch amp vs. 3 mono blocks or maybe a stereo amp plus a mono block for the center?

First, smart to only amplify only the front three channels. But to give you a meaningful answer, far more information is required. Such as what room is available for additional components, your budget and finally what kind of speakers you have. Do you really need 200 wpc?

Based on what you have provided, here are my comments. Three mono blocks reduces crosstalk and gives each speaker a dedicated power supply. These obviously are pros. But they take up more room and could be the most expensive option. A three channel amp obviously takes up the least room, a plus. The downside is it probably shares the same power supply. Is this a problem? Maybe or maybe not as now you have to consider budget. I would take a Parasound HALO A31 3 channel amp over three value priced (Outlaw, Emotiva, et al) mono blocks any day of the week.

Without knowing any of these factors, room, budget, and speakers I would now suggest something even a little more radical. You said you want the system to do double duty for HT & Music. I am assuming that you are talking about 2 channel stereo music. So I would scale down your power requirement (the 200 wpc) and get a 3 channel power amp around 100-150 wpc and a separate 2 channel PREAMP With HOME THEATER BYPASS. This will really improve your stereo music listening. experience more than the extra watts per channel ever could. Hope some of this helps.
It depends.
A 3 channel amp would be the easiest solution as far as electrical outlets(one plug instead of 3) and space on a stand/rack. Monoblocks might offer the best performance, though with a good 3-channel you'd be hard pressed to hear a difference.

It also might depend on your speaker model, with many types you might not need 200 wpc, or might need a more robust amp if they dip down to 2 ohms for example. Size of room and volume preferences would play a part as well.

I've got an Onkyo 876 that I use as a processor with an Outlaw Audio 7125(125 watts per 7 channels) and it's more than enough volume for my speakers and room. If the Integra has the sound characteristics similar to my flagship Onkyo, they are a bit on the forward or bright side in SQ. If your speakers are also on the bright or harsh side at high volumes, some amp brands could worsen the issue.
So, I got lucky and impulsive over the weekend and solved the amp issue. I found a heck of a deal on an Acurus A200x3 locally and brought it home.

I do like the suggestion of a 2-ch pre with HT pass through...especially since my wife wants me to get into vinyl.

The speakers that I am driving are almost finished and are a custom job by Selah Audio. They are less sensitive than what I have now (and sealed) but the drivers that we selected can take this amp and more...I wanted to ensure that there was ample headroom to get the most out of these speakers. they should end up somewhere between 4 and 6 ohms BTW.

Since I scored on the amp I need to look at some 2-ch pre-amps and see if I can get lucky again.

Budget for your preamp?
$500 or less, new or used.