eVersatile

I have been playing around with this for a little bit and have figured it out.
It has been a while since I wrote these lines and had to remind myself of why I did it that way.
Most custom post types that I make have their own seaerate comment.php file so I was unable to use it globally. Though, if you make one small change to the code and add it to the other comment.php file for your custom post type (assuming you have one), it should work.

global $post;
$args = array( 'psp_projects' => $post->ID );
$comment = get_comments( $args );
if ( 2 <= count( $comment ) ) {
    echo 'Comments Reached';
} else {
    comment_form();
}

Changing 'post_id' to 'projects' //(your post type) and placing the code in comments.php file for my projects then the code will work the same way for that post type.

Thanks for your reply Bill.
I do know about that alternative though it does not interest me.
I have came up with a solution.
If you implement this script:

global $post;
$args = array( 'post_id' => $post->ID );
$comment = get_comments( $args );
if ( 3 <= count( $comment ) ) {
    echo '';
} else {
    comment_form();
}

in comments.php file then no more comments will be allowed after 3 submissions.
I will mark this topic as resolved.

I am using the Xphoria theme. Would this section of script be what I’m looking for?

.blog-post { padding-bottom:60px; margin-bottom:10px; display:table; width:100%; border-bottom:1px solid #262626; }
.single-post .blog-post { padding-bottom:50px; }
.post-title { margin-bottom:50px; position:relative; border-bottom:1px solid #262626; }
.post-title h1 { line-height:58px; margin:0px; padding:20px 0px; }
.post-title a { color:#feff89; font-size:48px; font-family:Dosis; }
.comments-number { position:absolute; right:0px; bottom:20px; height:35px; text-align:right; font-size:30px; line-height:1.0em; padding-left:38px; background-image: url( "images/comment.png" ); background-repeat: no-repeat; background-position:0px 4px; }
.post-category { position:absolute; left:0px; bottom:-12px; padding-right:3px; background:#1c1919; text-transform:uppercase; }
.post-category a { font-size:12px; font-weight:bold; color:#ffffff; line-height:1.0em; padding:1px 4px 1px 4px; background:#d12020; }
.more-link { float:right; margin-top:30px; }
.single-post .blog-post { margin-bottom:50px; }
.subtitle { margin-bottom:5px; font-size:22px; font-weight:500; margin-bottom:50px; }
.text img, .text .wp-caption { max-width:750px!important; height:auto!important; }
.text .entry p { margin-bottom: 25px; }
.text .entry ul { list-style-type:circle; margin:0 0 20px 30px; }
.text .entry ol { list-style-type: decimal; margin:0 0 20px 30px; }
.text .entry p a, .comment-entry p a { text-decoration:underline; transition: all 300ms ease-in; }
.text .entry p a:hover, .comment-entry p a:hover { color:#f98536;}
div.thumbnail { margin:7px 27px 0px 0; float:left; text-align:center; }
.no-thumbnail { width:90px; height:110px; float:left; position:relative; overflow:hidden; margin:8px 0px 0px 0; }
div.thumbnail span { padding:3px 5px; background:#d12020; font-size:11px; text-align:left; float:left; line-height:1.0em; }
div.thumbnail img { border:14px solid #131111; display:block; }
.blog-post-left { width:65px; text-align:center; position:absolute; background:#1c1919; padding-right:12px; padding-bottom:12px; border-right:14px solid #131111; border-bottom:14px solid #131111; }
.no-thumbnail .blog-post-left { border-right:none; border-bottom:none; width:95px; background:none; }
.blog-post-left-date { width:65px; padding:8px 0; background:#232323; border-top:1px solid #333232; border-left:1px solid #333232; border-right:1px solid #333232; }
.blog-post-left-month { font-size:18px; line-height:1.1em; text-transform:uppercase; }
.blog-post-left-day { font-size:36px; line-height:1.1em; }
.blog-post-left-author { background:#6c2b9d; font-size:13px; border:1px solid #934cc8; width:65px; }
.prev-post a, .next-post a { display:block; padding:7px 11px; margin-top:40px; margin-bottom:20px; border-radius:6px; font-size:11px; background:#e8e8e8;  }
.post-details-tags a { font-size:16px; padding:5px 9px; background:#202020; border:1px solid #2c2b2b; }

Found within /wp-content/themes/Xphoria/style.css