Use a new CSS file to override current website's CSS

My website has currently 3 CSS files that are automatically included as a part of the website and I do not have access to the source i.e. index.html of the website but I do have access to the CSS files of my website.

I am trying to use my own style to override my websites CSS files and create a new CSS file that would contain all the styling that I would like to overwrite on my website.

I have tried using @import url(css4.css) and I have placed that at the top of my last CSS file but that wouldn't overwrite the last CSS file's styling.

How can I achieve this?

<link rel="stylesheet" type="text/css" href="currentCSS1.css">
<link rel="stylesheet" type="text/css" href="currentCSS2.css">
<link rel="stylesheet" type="text/css" href="currentCSS3.css">   
<!-- How to add this below just by using CSS? -->
<link rel="stylesheet" type="text/css" href="newCSS4.css">

Besides using !important that most answers are advising you to use, this is a matter of CSS specificity

The concept

Specificity is the means by which a browser decides which property values are the most relevant to an element and gets to be applied. Specificity is only based on the matching rules which are composed of selectors of different sorts.

How is it calculated?

The specificity is calculated on the concatenation of the count of each selectors type. It is a weight that is applied to the corresponding matching expression.

In case of specificity equality, the latest declaration found in the CSS is applied to the element.

Some rules of thumb

Never use !important on site-wide css.

Only use !important on page-specific css that overrides site-wide or foreign css (from ExtJs or YUI for example).

Never use !important when you're writing a plugin/mashup.

Always look for a way to use specificity before even considering !important

can be represented by 4 columns of priority:

inline = 1|0|0|0

id = 0|1|0|0

class = 0|0|1|0

element = 0|0|0|1

Left to right, the highest number takes priority.

Here is a snippet with a Full example of a CSS specificity

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}

/*CSS Specificity */

/* SPECIFICITY: 0/1/0/0 */
#id {
  background-color: green
}

/* SPECIFICITY: 0/0/1/0 */
.class {
  background-color: yellow 
}

/* SPECIFICITY: 0/0/0/1 */
section {
  background-color: blue 
}
  
/* ------------ override inline styles ----------- */

/*to override inline styles we  now use !important */

/* SPECIFICITY  0/0/1/0 */

.inline {
  background-color: purple !IMPORTANT /*going to be purple - final result */ 
}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div class="inline" style="background-color:red">
          <!--SPECIFICITY 1/0/0/0 - overridden by "!important -->
        </div>
      </section>
    </div>
  </div>
</article>

Now here is the Full snippet step by step

ID: GREEN

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}

/*CSS Specificity */

/* SPECIFICITY 0/1/0/0 */
#id {
  background-color: green
}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div>             
        </div>
      </section>
    </div>
  </div>
</article>

CLASS: YELLOW

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}

/*CSS Specificity */

/* SPECIFICITY  0/0/1/0 */
.class {
  background-color: yellow
}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div>
        </div>
      </section>
    </div>
  </div>
</article>

ELEMENT: BLUE

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}

/*CSS Specificity */

/* SPECIFICITY  0/0/0/1 */
section {
  background-color: blue
}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div>
        </div>
      </section>
    </div>
  </div>
</article>

INLINE STYLE: RED

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div style="background-color:red">
        <!--SPECIFICITY 1/0/0/0 -->
        </div>
      </section>
    </div>
  </div>
</article>

OVERRIDDEN INLINE STYLE: PURPLE

/*demo purposes*/
body {margin: 0;padding: 0}
div,article {min-height: 200px;height: 100%;width: 100%}
/*CSS Specificity */

/* SPECIFICITY  1/0/0/1 */

section > div {
  background-color: purple !IMPORTANT
}

<article>
  <div id="id">
    <div class="class">
      <section>
        <div style="background-color:red">
        <!--SPECIFICITY 1/0/0/0 -->
        </div>
      </section>
    </div>
  </div>
</article>

You can calculate the specificity of your element(s) here

Note:

A must read on this subject

Inheritance and cascade
CSS Specificity
Specifics on CSS Specificity

Here's a fun solution no one has mentioned.

Facts:

You cannot modify the HTML of the page at all - no problem!
You can modify the CSS files, but the developers may modify them again later and remove any changes you made - not a worry.
You cannot/do not want to use Javascript and JQuery - fine by me.
You can add more files on to the server - Excellent!

Let's do some .htacess hacking for fun and profit!

Document root .htaccess file:

Options +FollowSymlinks
RewriteEngine on
RewriteBase /

RewriteRule ^(.*?)css3.css(.*?) $1hackedCSS3.php$2 [L]

Result: hackedCSS3.php is silently served instead of css3.css on every request.

REF: http://httpd.apache.org/docs/2.2/howto/htaccess.html

hackedCSS3.php file:

<?php

// Send the right header information!
header("Content-type: text/css; charset: UTF-8");

// Output the css3.css file
echo file_get_contents("css3.css");
?>

// Add your CSS here with any neat !important or override tricks (read: specificity)
div { ... }

Bonus:

You could expand this solution to include all three .css files in this one .php file (but only serve, say, css3.css and send the css1.css and css2.css to a black hole with .htaccess), and use clever regular expressions to remove/modify those developer's CSS without touching any of their files. The possibilities are tantalizing.

Addendum:

Can you be a bit more specific on where to include these files?

The .htaccess file should be in the document root directory of the website. This is where www.example.com/index.html would load index.html

Should the hackedCSS3.php file be in the same directory as the other css files?

It can be in any directory you specify in the .htaccess file. The document root is fine. Change

RewriteRule ^(.*?)css3.css(.*?) $1hackedCSS3.php$2 [L]

RewriteRule ^(.*?)css3.css(.*?) /folders/you/want/hackedCSS3.php$2 [L]

Should our css content (where you specified // Add your CSS here...) should be within html style tags?

No. Treat your CSS code in that section as if it were a .css file. You do not need <style> tags.