Stuck Fermentation Recovery

I recently brewed an IPA OG 1.078 and FG 1.028. The final was measured over several days and never moved, I expected it to drop to at least 1.020. I ended up bottling as fermentation had stopped (10 days in primary, 2 weeks in secondary) but was wondering what do I risk by adding more yeast? My assumption is I would reach the target FG but what about taste? Do the yeast strains need to be consistent?

You may not reach you estimated FG depending on the amount of unfermentable sugars in your wort. According to your numbers that is about 62% attenuation, which is a little low (depending on yeast used).

Adding more of the same yeast probably wont make a significant difference, since the yeast stalled or didn't ferment down to where you had expected.

Try rousing your yeast by swirling your fermenter and allowing the temps to rise to about 68-70°, if that doesn't work in itself, add some yeast nutrient/energizer and gently stir with a sanitized stirring utensil, if all else fails then try adding more yeast, preferably a strain with a higher attenuation than your original yeast, however, adding a different yeast strain will definitely impact your flavor profile.

The yeast strains don't have to be consistent, but you should use something neutral for the second addition if needed.

I have never added additional yeast but I heard from White Labs directly that adding yeast to an existing already fermented beer might not work unless that yeast is actively metabolizing sugar. (I.e. make a starter and add when active.) Otherwise you could dump in yeast and it might just settle out immediately and never do anything.

Again - i've never done it, either way, but it's well documented.