Go for it.....its your hair and you only live once.
75% of problems with color come from coloring hair that has NO business being colored. The other 25% of problems comes from the care afterwards. You can not treat color treated relaxed hair the exact same way you treated it before the color. No way, ain't happening
The needs of double processed hair are different and you have to be prepared to cater to those new needs. For example, if you already relax your hair bone straight and now you want to be a level 6 blond
Hecky no
Color Treated hair needs milder relaxers so if you are contemplating coloring, you already need to be making the switch to a milder relaxing result. If you can't put in the commitment after the color then don't do it. This means the extra conditioning time each week, the reduction of heat, the use of quality products designed to preserve the intergrity of the hair, especially color treated hair, and the knowledge to do your own troubleshooting and the patience to work through the problems until you find your stride.
This is also when you have to be careful not to bite off more than you can chew. If you already have problems deep conditioning on a regular basis then a head full of highlights and an overall shade lift isn't for you. Try a semi-permanent rinse instead. You also need to make sure that you are going to a colorist and not a regular ol' stylist. Colorist have additional training to do color. Mixing shades and color placement to compliment your undertones, your hair style and texture, your maintance scheldule etc..... these are things that colorist get more training in assessing. Yes they will usually cost more but the result is worth it 90% of the time. When you choose to do it at home, you need to have an understanding of color, how it does what it does, and you don't need to attempt to lift more than 2 levels at home.
I love color and I have since recently colored my hair after 3 years and I plan on keeping it colored in some form or fashion from now on. You can successfully color and still pursue longer hair but you have to make the commit to do so.