Hi,
I have read your exact requirement in which you have mentioned that you want your existing site should be more speedup.
Please share the URL of the site so I can check the current performance and issues on Google Page speed.
I will optimize the complete site and server so the load time will be reduced and will achieve a very good score for mobile and desktop both.
Query: Do you have shared Hosting or Dedicated server?
Following some steps so we can increase the speed of the site:
1. Compression
2. Caching (in caching ...page speed, varnish, Redis if root detail available)
3. Leverage browser caching
4. Optimize images minify CSS and JS.
5. Add expires headers
6. Database optimization
7. Setup CDN, etc
Regards
Karuna