Can I have multiple Google Site Verification TXT records on one domain?

Adding multiple TXT records will function correctly. You can see some high profile companies doing that e.g. microsoft.com

$ dig -t txt @8.8.8.8 microsoft.com

; <<>> DiG 9.10.6 <<>> -t txt @8.8.8.8 microsoft.com
; (1 server found)
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 42907
;; flags: qr rd ra; QUERY: 1, ANSWER: 13, AUTHORITY: 0, ADDITIONAL: 1

;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 512
;; QUESTION SECTION:
;microsoft.com.         IN  TXT

;; ANSWER SECTION:
microsoft.com.      2744    IN  TXT "adobe-idp-site-verification=8aa35c528af5d72beb19b1bd3ed9b86d87ea7f24b2ba3c99ffcd00c27e9d809c"
microsoft.com.      2744    IN  TXT "google-site-verification=yUE_SrjKKb4FHH1H04VWidfwstTGeS1FLx3Mcsnijjs"
microsoft.com.      2744    IN  TXT "adobe-sign-verification=c1fea9b4cdd4df0d5778517f29e0934"
microsoft.com.      2744    IN  TXT "docusign=d5a3737c-c23c-4bd0-9095-d2ff621f2840"
microsoft.com.      2744    IN  TXT "FbUF6DbkE+Aw1/wi9xgDi8KVrIIZus5v8L6tbIQZkGrQ/rVQKJi8CjQbBtWtE64ey4NJJwj5J65PIggVYNabdQ=="
microsoft.com.      2744    IN  TXT "v=spf1 include:_spf-a.microsoft.com include:_spf-b.microsoft.com include:_spf-c.microsoft.com include:_spf-ssg-a.microsoft.com include:spf-a.hotmail.com ip4:147.243.128.24 ip4:147.243.128.26 ip4:147.243.1.153 ip4:147.243.1.47 ip4:147.243.1.48 -all"
microsoft.com.      2744    IN  TXT "atlassian-domain-verification=jbey7I2+3Wyl+PZ0QUCC6fCz2Gu5KO7GQPcy/0c4za7ebQxar/qqujJH4kZLVQHZ"
microsoft.com.      2744    IN  TXT "google-site-verification=8-zFCaUXhhPcvN29EVw2RvtASDCaDPQ02L1HJ8Om8I0"
microsoft.com.      2744    IN  TXT "facebook-domain-verification=gx5s19fp3o8aczby6a22clfhzm03as"
microsoft.com.      2744    IN  TXT "google-site-verification=6P08Ow5E-8Q0m6vQ7FMAqAYIDprkVV8fUf_7hZ4Qvc8"
microsoft.com.      2744    IN  TXT "facebook-domain-verification=bcas5uzlvu0s3mrw139a00os3o66wr"
microsoft.com.      2744    IN  TXT "docusign=52998482-393d-46f7-95d4-15ac6509bfdd"
microsoft.com.      2744    IN  TXT "facebook-domain-verification=m54hfzczreqq2z1pf99y2p0kpwwpkv"

;; Query time: 45 msec
;; SERVER: 8.8.8.8#53(8.8.8.8)
;; WHEN: Tue Jun 25 23:29:46 CST 2019
;; MSG SIZE  rcvd: 1258

A simple workaround is to use a different form of identification. Google enables you to verify yourself using different methods, such as uploading a file to the server, or changing a meta tag. You can check all the available methods here:

https://support.google.com/webmasters/answer/9008080?hl=en