Certainly one may go to a protestant church in addition to attending Catholic Mass, even regularly if, for example, one is a musician and plays/sings at the protestant church.
But it’s a fine line about the ‘more social manner’. Because you see there is then a danger that has already come into your mind, the idea that the protestant venue is ‘more social’ than the Catholic one AND the idea that one gets more out of ‘worshipping in a more social manner’. That actually winds up taking the worship (of God) and turning it into a worship of the worship, i.e., the protestant church has things which appeal to me more so I need to satisfy my own need to do appealing things.
If your best friend or spouse or other family member attends the protestant church and you like to go because that person is there to worship with, or there’s a lot of family and friends, that’s one thing. The ‘social’ is with a group that you ‘already’ socialize with.
But if you just know people casually but you like the way that everybody seems to act, all the neat things they offer, the whole worship ‘style’, the friendly, relaxed, ‘we’re so glad you’re here’, and you are contrasting that with the cold, formal, solitary, "I’ve gone to this church for 5 years, nobody says anything to me’ Catholic church and going, “Pfui on these cold-hearted rigid sourpuss slugs! I deserve better, I’ll show up for my ‘duty’ and then get out where I’ll get some real fellowship, fun, and experience God the 'right way”, then it’s a problem.
Now you might spend the rest of your life going to St.Sourpuss. You might grit your teeth and hate it. You have two choices, you can try to be St Sweetness and get things going that way (knowing it might take AGES for people to respond, if ever), or you might just throw up your hands, "Lord, you know I find this behavior hard to deal with. But Lord, while I might have a more positive attitude than all the other people here, I’ve got my own sins and faults that they–and everybody else–have to put up with. While I’m carping that they are rigid and cold, they might be thinking, "oh no, here comes that loud, over-the-top person again, always trying to get people to ‘act happy’. We don’t want to be fake! We ARE perfectly happy, but we show it in quieter ways. We keep trying to model this, but that person doesn’t seem to get it. Lord, you know we find this behavior hard to deal with. . " IOW, oops, when we think we have the right attitude and somebody else is doing it wrong, they might be thinking the same about us. . .and perhaps we BOTH have an attitude that is perfectly fine.
So maybe we need to be sure that we really enjoy going to the Catholic Church first and ONLY then might we want to think about worshipping ‘elsewhere’.