It can be hard to quantify what exactly constitutes a "simplification" of linguistic structures. Linguists generally try to avoid conceptualizing language change as a simplification or as a complication; we try and think of linguistic change as just being that, change. Language is a dynamic and adaptive system, and individuals often adjust their communication strategies based on the context and their interlocutors. The impact of multilingualism on language complexity is likely influenced by various factors, including the nature of language contact, the linguistic diversity within the community, and individual language learning experiences. The variables which affect linguistic change are enormous, and usually occurring over long periods of time .
That being said, there are plenty of observable and well-documented examples of languages convergence and languages affecting each other. You could think of pidgins, rudimentary languages created due to the need for a common language between two speech communities. You could think of things like Spanglish, a hybrid language that has developed in communities where Spanish and English speakers interact extensively, such as in the United States, and you could think of languages like Chiac in Canada which is often said to be a "combination" of French and English.
Then, you have examples of more major structural change occurring between languages in (prolonged) mutual contact. One example that comes to mind is Greek. Greek is inherently an SVO language. There are Greek speakers in Turkey. Turkish is an SOV language. It is documented that Greek spoken in Turkey has become, largely, SOV due to its interaction with the Turkish language. Is this a simplification? Again, hard to define. But it is surely a result of the two languages' contact. There are plenty of examples of things like this.
Now, getting a bit back to your specific question about multilinguals. It's highly unlikely that that your L1 was damaged in any way due to having to simplify your language in conversation with non-native speakers. I've seen longitudinal studies that show how overtime ones L1 can be changed due to language dominance. For example, I remember a longitudinal study on a Cuban-born L1 Spanish speaker who used the subjunctive mood in her Spanish significantly less later in her life; they hypothesized this was due to her living her life primarily in English after moving to Miami.
But the situation that you are describing would not facilitate such a change. As a master's student in Applied Ling (and I have my bachelors in the same subject), I have never come across a study of the sort which seeks to investigate the "simplification," or the loss of vocabulary, or the loss of any other linguistic feature, in multilingual speakers, besides ones along the lines of what I described with the Cuban woman.
