Would adding a separate 3 channel help in this situation

I have an Anthem 1120 receiver running a 5.1.4 system. My front speakers are Paradigm 85F with a Paradigm 55 C as center channel. When I play a movie with a lot of heavy sound effects the sound gets really loud during the sound effects and my family objects when it get very loud. If I added a 3 channel amp can I play at a lower volume and be able to hear and understand the dialogue. I start at a fairly loud but not blasting level to hear the dialogue clearly. I want to still be able to enjoy the sound effects but at a lower volume setting. Thanks
The answer is "It depends".  I don't know that playing at a lower volume will necessarily give you better clarity.  A better amp could possibly give you this, but the Anthem receivers are generally very clean and bright sounding anyways.

It could also be that your family is more sensitive to clipping distortion that happens when you overdrive an amp (or in this case your receiver with an inadequate power supply).  Putting in a beefy high current 3-channel amplifier will definitely help clean up the sound.  With a clean system like this, the listeners will generally not realize how loud it is (because it's so clean and natural sounding).

On an under powered amp (such as a receiver), when those sound effects start going off and things get loud, these low end amps do not have beefy enough power supplies to provide clean power on these higher voltage outputs.  At this point, the clarity in the sound and "separation of instruments" goes to hell. The dialog becomes a mess because the amp cannot keep a clean power supply voltage when the output goes into the "hundreds of watts" area.

The lacking of clarity on the dialog could also be from acoustic reflections in your room.  Getting some acoustic panels (such as GIK Acoustics) and placing them properly could actually increase the level of clarity (and in some cases the perceived loudness) of the dialog.  In a room with lots of reflected sound, the dialog becomes a mess and it's actually very hard to hear and understand the words of the actors.
My receiver is excellent, Anthem 1120, so distortion is not the problem. The sound is great, I have a Paradigm X-15 Defiance sub, its just that the sound goes way up anytime there is any kind of special effect sound. I thought an amp running the front end could make a difference as I read that somewhere but I don't want to spend the money without having opinions of people who run a separate amp for the front speakers. Thanks
You should look into the built-in compression settings.  I'm not sure what it's called but you can reduce the dynamic range.
Also, while the ARC is pretty good, you might want to boost the center channel somewhat.
Of course good room acoustics help. :)
Just get a compander. Movies are mixed for big rooms like theaters.
Even a Terk VR-1 will help but you can do much better.
Move into a barn.
I cannot fathom how adding an amp & speakers would limit dynamic range.
Enlighten me.
I am curious about this as well...same aggravation with the cohabitants here.  I have an upper end Marantz Receiver and Focal 936 and other Focal in wall/ceiling speakers, all calibrated through the room correction.  Voice levels are not quite loud enough so up goest he volume...until the effects start going off and then it is too loud for the others.  This is MOST notable when playing UHD.  
Per the other poster, I probably just need to bump up the center channel...not sure why I haven't done that yet.  
To the OP, my first inclination was to get better amp for this system...hahah..probably need to do that anyway as that is what this hobby is all about.
Ah, Erik, that's an excellent suggestion.  I forgot about that.  Looking at manual, the Anthem has a "DYN" button on the remote.  Just hit the DYN button twice, then you can choose between 3 dynamic range settings:

NORMAL: No dynamic range modification.

REDUCED: Allows the quieter parts to be heard more easily by raising the level of quieter sounds and/or reducing the level of louder ones according to cues in the soundtrack.

LATE NIGHT: Further reduces the softest-to-loudest difference

I'm sure you can play with these to determine which one is best for you.

Also, asnumcwrt2 suggested, try bumping up the center channel by 1 db.  You would be amazed at the increased vocal clarity when you do a 1 db or 2 db adjustment on the center channel.  NOTE: this may put the center out of calibration based on keeping it exact as the left/right/surround, but I have seen an increase in understanding dialog when I do this - and it really doesn't detract from any sound balance.
@numcwrt2 - Marantz receivers has the dynamic range compression feature as well.  If you go into the setup menu, it is under Settings => Audio => Surround Paramater => Dynamic Compression.

You should play with the Low / Medium / High settings here.
I know we are not talking exacts here but when I first added a 200w/ch B&K 3-channel amp to run my LCR and let my midlevel Onkyo AVR just drive the surrounds, low level listening improved in very noticeable ways in my 4800ft3 multi-use room. Most improvement was with dialog detail.

@willland Thanks for that information. I also have a large multi use room. I will talk to my Paradigm dealer about it and see if I can try out the Paradigm 3 channel amp before buying