How can I use my template in a pipeline definition that extends a template from another repository?

I have a pipeline that extends a template from another repository. That external template takes a stageList called stages.

My pipeline:

resources:
  repositories:
    - repository: templates
      type: git
      name: OtherProject/OtherRepo
      ref: refs/heads/main

extends:
  template: BaseTemplate.yml@templates

  stages:
  - stage: build
    jobs:
    - job: main
      steps:

My steps include some localization, where I need to execute a task for each language. I currently have each language manually defined as a separate task:

- task: MSBuild@1
  displayName: 'Build (de-DE)'
  inputs:
    solution: '$(Build.SourcesDirectory)\MyProject.wixproj'
    msbuildArguments: '/p:Cultures="de-DE"
    ...more args, 15 lines long...

...repeated for each language. Gross.

So I'd like to try to use templates for this. But when I move the MSBuild task to another file and try

- template: ./templates/localizedBuild.yml
  parameters:
    language: 'de-DE'

then ADO gives me this error when I go to queue up a pipeline run:

The 'stages' parameter is not a valid StageList. /.pipelines/MyPipeline.yml: File /templates/localizedMsi.yml not found in repository https://company.visualstudio.com/OtherProject/_git/OtherRepo

As I understand it, this is because paths to templates are calculated relative to the file doing the including... which is the BaseTemplate.yml file, not MyPipeline.yml.

Is there a way to indicate in the yml that I'm trying to reference a template in my repo?